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148-519: A black hole is a region of spacetime wherein gravity is so strong that no matter or electromagnetic energy (e.g. light ) can escape it. Albert Einstein 's theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon . A black hole has a great effect on the fate and circumstances of an object crossing it, but it has no locally detectable features according to general relativity. In many ways,

296-402: A gravity assist to siphon kinetic energy away from large bodies. Precise trajectory calculations require taking into account small forces like atmospheric drag , radiation pressure , and solar wind . A rocket under continuous or intermittent thrust (or an object climbing a space elevator ) can attain escape at any non-zero speed, but the minimum amount of energy required to do so is always

444-481: A is the semi-major axis , which is infinite for parabolic trajectories. If the body has a velocity greater than escape velocity then its path will form a hyperbolic trajectory and it will have an excess hyperbolic velocity, equivalent to the extra energy the body has. A relatively small extra delta- v above that needed to accelerate to the escape speed can result in a relatively large speed at infinity. Some orbital manoeuvres make use of this fact. For example, at

592-403: A parabola whose focus is located at the center of mass of the planet. An actual escape requires a course with a trajectory that does not intersect with the planet, or its atmosphere, since this would cause the object to crash. When moving away from the source, this path is called an escape orbit . Escape orbits are known as C3 = 0 orbits. C3 is the characteristic energy , = − GM /2 a , where

740-424: A speed than a velocity because it is independent of direction. Because gravitational force between two objects depends on their combined mass, the escape speed also depends on mass. For artificial satellites and small natural objects, the mass of the object makes a negligible contribution to the combined mass, and so is often ignored. Escape speed varies with distance from the center of the primary body, as does

888-448: A . The pulse is reflected from a mirror situated a distance a from the light source (event Q), and returns to the light source at x ′ = 0,  ct ′ =  a (event R). The same events P, Q, R are plotted in Fig. 2-3b in the frame of observer O. The light paths have slopes = 1 and −1, so that △PQR forms a right triangle with PQ and QR both at 45 degrees to

1036-461: A November 1783 letter to Henry Cavendish , and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke , who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta , notorious as a prison where people entered but never left alive. The term "black hole"

1184-505: A black hole acts like an ideal black body , as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation , with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes , making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for light to escape were first considered in

1332-504: A black hole appears to slow as it approaches the event horizon, taking an infinite amount of time to reach it. At the same time, all processes on this object slow down, from the viewpoint of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift . Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than

1480-461: A black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Any matter that falls toward a black hole can form an external accretion disk heated by friction , forming quasars , some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed." If other stars are orbiting

1628-512: A black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M , through where r s is the Schwarzschild radius and M ☉ is the mass of the Sun . For a black hole with nonzero spin and/or electric charge, the radius is smaller, until an extremal black hole could have an event horizon close to The defining feature of a black hole

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1776-519: A black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems and established that the radio source known as Sagittarius A* , at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses. The idea of

1924-450: A body so big that even light could not escape was briefly proposed by English astronomical pioneer and clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that one would form when a star's diameter exceeds the Sun's by a factor of 500, and its surface escape velocity exceeds

2072-403: A closed shape, it can be referred to as an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the trajectory will be equal to the escape velocity at that point due to the conservation of energy, its total energy must always be 0, which implies that it always has escape velocity; see the derivation above. The shape of the trajectory will be

2220-404: A density as the Sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the spacetime metric that space would close up around

2368-445: A fourth dimension, it is treated differently than the spatial dimensions. Minkowski space hence differs in important respects from four-dimensional Euclidean space . The fundamental reason for merging space and time into spacetime is that space and time are separately not invariant, which is to say that, under the proper conditions, different observers will disagree on the length of time between two events (because of time dilation ) or

2516-420: A geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space . This interpretation proved vital to the general theory of relativity , wherein spacetime is curved by mass and energy . Non-relativistic classical mechanics treats time as a universal quantity of measurement that is uniform throughout,

2664-453: A great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery. Minkowski had been concerned with

2812-405: A higher potential energy than this cannot be reached at all. Adding speed (kinetic energy) to an object expands the region of locations it can reach, until, with enough energy, everywhere to infinity becomes accessible. The formula for escape velocity can be derived from the principle of conservation of energy. For the sake of simplicity, unless stated otherwise, we assume that an object will escape

2960-574: A light signal in that same time interval Δ t {\displaystyle \Delta t} . If the event separation is due to a light signal, then this difference vanishes and Δ s = 0 {\displaystyle \Delta s=0} . When the event considered is infinitesimally close to each other, then we may write In a different inertial frame, say with coordinates ( t ′ , x ′ , y ′ , z ′ ) {\displaystyle (t',x',y',z')} ,

3108-434: A location. In Fig. 1-1, imagine that the frame under consideration is equipped with a dense lattice of clocks, synchronized within this reference frame, that extends indefinitely throughout the three dimensions of space. Any specific location within the lattice is not important. The latticework of clocks is used to determine the time and position of events taking place within the whole frame. The term observer refers to

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3256-425: A low Earth orbit of 200 km). The required additional change in speed , however, is far less because the spacecraft already has a significant orbital speed (in low Earth orbit speed is approximately 7.8 km/s, or 28,080 km/h). The escape velocity at a given height is 2 {\displaystyle {\sqrt {2}}} times the speed in a circular orbit at the same height, (compare this with

3404-471: A mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. The first black hole known was Cygnus X-1 , identified by several researchers independently in 1971. Black holes of stellar mass form when massive stars collapse at

3552-442: A mere shadow, and only some sort of union of the two shall preserve independence." Space and Time included the first public presentation of spacetime diagrams (Fig. 1-4), and included a remarkable demonstration that the concept of the invariant interval ( discussed below ), along with the empirical observation that the speed of light is finite, allows derivation of the entirety of special relativity. The spacetime concept and

3700-464: A non-stable but circular orbit around the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable , hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross

3848-419: A person moving with respect to the first observer will see the two events occurring at different places, because the moving point of view sees itself as stationary, and the position of the event as receding or approaching. Thus, a different measure must be used to measure the effective "distance" between two events. In four-dimensional spacetime, the analog to distance is the interval. Although time comes in as

3996-400: A place where escape speed is 11.2 km/s, the addition of 0.4 km/s yields a hyperbolic excess speed of 3.02 km/s: If a body in circular orbit (or at the periapsis of an elliptical orbit) accelerates along its direction of travel to escape velocity, the point of acceleration will form the periapsis of the escape trajectory. The eventual direction of travel will be at 90 degrees to

4144-421: A positive speed.) An object on a parabolic trajectory will always be traveling exactly the escape speed at its current distance. It has precisely balanced positive kinetic energy and negative gravitational potential energy ; it will always be slowing down, asymptotically approaching zero speed, but never quite stop. Escape velocity calculations are typically used to determine whether an object will remain in

4292-492: A second. On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle . The topology of

4440-413: A single point in spacetime. Although it is possible to be in motion relative to the popping of a firecracker or a spark, it is not possible for an observer to be in motion relative to an event. The path of a particle through spacetime can be considered to be a sequence of events. The series of events can be linked together to form a curve that represents the particle's progress through spacetime. That path

4588-402: A spacecraft will accelerate steadily out of the atmosphere until it reaches the escape velocity appropriate for its altitude (which will be less than on the surface). In many cases, the spacecraft may be first placed in a parking orbit (e.g. a low Earth orbit at 160–2,000 km) and then accelerated to the escape velocity at that altitude, which will be slightly lower (about 11.0 km/s at

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4736-433: A spacetime diagram illustrating the world lines (i.e. paths in spacetime) of two photons, A and B, originating from the same event and going in opposite directions. In addition, C illustrates the world line of a slower-than-light-speed object. The vertical time coordinate is scaled by c {\displaystyle c} so that it has the same units (meters) as the horizontal space coordinate. Since photons travel at

4884-490: A spatial distance Δ x . {\displaystyle \Delta x.} Then the squared spacetime interval ( Δ s ) 2 {\displaystyle (\Delta {s})^{2}} between the two events that are separated by a distance Δ x {\displaystyle \Delta {x}} in space and by Δ c t = c Δ t {\displaystyle \Delta {ct}=c\Delta t} in

5032-540: A student of Hendrik Lorentz , independently gave the same solution for the point mass and wrote more extensively about its properties. This solution had a peculiar behaviour at what is now called the Schwarzschild radius , where it became singular , meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that

5180-414: A wave rather than a particle, it was unclear what, if any, influence gravity would have on escaping light waves. The modern theory of gravity, general relativity, discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface. Instead, spacetime itself is curved such that

5328-626: A year before his death), Minkowski introduced his geometric interpretation of spacetime in a lecture to the Göttingen Mathematical society with the title, The Relativity Principle ( Das Relativitätsprinzip ). On 21 September 1908, Minkowski presented his talk, Space and Time ( Raum und Zeit ), to the German Society of Scientists and Physicians. The opening words of Space and Time include Minkowski's statement that "Henceforth, space for itself, and time for itself shall completely reduce to

5476-408: Is "invariant". In special relativity, however, the distance between two points is no longer the same if measured by two different observers, when one of the observers is moving, because of Lorentz contraction . The situation is even more complicated if the two points are separated in time as well as in space. For example, if one observer sees two events occur at the same place, but at different times,

5624-415: Is a measure of separation between events A and B that are time separated and in addition space separated either because there are two separate objects undergoing events, or because a single object in space is moving inertially between its events. The separation interval is the difference between the square of the spatial distance separating event B from event A and the square of the spatial distance traveled by

5772-419: Is actually what is indicated by moving clocks by applying an explicitly operational definition of clock synchronization assuming constant light speed. In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity . In 1905/1906 he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with

5920-408: Is called an event , and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig. 1). An event is represented by a set of coordinates x , y , z and t . Spacetime is thus four-dimensional . Unlike the analogies used in popular writings to explain events, such as firecrackers or sparks, mathematical events have zero duration and represent

6068-550: Is called the particle's world line . Mathematically, spacetime is a manifold , which is to say, it appears locally "flat" near each point in the same way that, at small enough scales, the surface of a globe appears to be flat. A scale factor, c {\displaystyle c} (conventionally called the speed-of-light ) relates distances measured in space to distances measured in time. The magnitude of this scale factor (nearly 300,000 kilometres or 190,000 miles in space being equivalent to one second in time), along with

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6216-402: Is defined to be zero a long distance away from a planet, so The same result is obtained by a relativistic calculation, in which case the variable r represents the radial coordinate or reduced circumference of the Schwarzschild metric . An alternative expression for the escape velocity v e {\displaystyle v_{e}} particularly useful at the surface on

6364-588: Is identical to that of any other body of the same mass. Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric , while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum. While

6512-562: Is no preferred origin, single coordinate values have no essential meaning. The equation above is similar to the Pythagorean theorem, except with a minus sign between the ( c t ) 2 {\displaystyle (ct)^{2}} and the x 2 {\displaystyle x^{2}} terms. The spacetime interval is the quantity s 2 , {\displaystyle s^{2},} not s {\displaystyle s} itself. The reason

6660-514: Is positive, the spacetime interval is referred to as timelike . Since spatial distance traversed by any massive object is always less than distance traveled by the light for the same time interval, positive intervals are always timelike. If s 2 {\displaystyle s^{2}} is negative, the spacetime interval is said to be spacelike . Spacetime intervals are equal to zero when x = ± c t . {\displaystyle x=\pm ct.} In other words,

6808-521: Is referred to as the second cosmic velocity . For a body in an elliptical orbit wishing to accelerate to an escape orbit the required speed will vary, and will be greatest at periapsis when the body is closest to the central body. However, the orbital speed of the body will also be at its highest at this point, and the change in velocity required will be at its lowest, as explained by the Oberth effect . Escape velocity can either be measured as relative to

6956-517: Is relative to a non-rotating frame of reference, not relative to the moving surface of the planet or moon, as explained below. The escape velocity relative to the surface of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator , a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to

7104-412: Is separate from space, and is agreed on by all observers. Classical mechanics assumes that time has a constant rate of passage, independent of the observer's state of motion , or anything external. It assumes that space is Euclidean : it assumes that space follows the geometry of common sense. In the context of special relativity , time cannot be separated from the three dimensions of space, because

7252-589: Is that unlike distances in Euclidean geometry, intervals in Minkowski spacetime can be negative. Rather than deal with square roots of negative numbers, physicists customarily regard s 2 {\displaystyle s^{2}} as a distinct symbol in itself, rather than the square of something. In general s 2 {\displaystyle s^{2}} can assume any real number value. If s 2 {\displaystyle s^{2}}

7400-473: Is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine whether such an event occurred. As predicted by general relativity,

7548-408: Is the only vacuum solution that is spherically symmetric . This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore correct only near a black hole's horizon; far away, the external gravitational field

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7696-455: Is the ratio of the original speed v {\displaystyle v} to the escape velocity v e . {\displaystyle v_{e}.} Unlike escape velocity, the direction (vertically up) is important to achieve maximum height. If an object attains exactly escape velocity, but is not directed straight away from the planet, then it will follow a curved path or trajectory. Although this trajectory does not form

7844-544: Is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17  M ☉ . Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. The hypothetical collapsed stars were called "frozen stars", because an outside observer would see

7992-400: The c t {\displaystyle ct} -coordinate is: or for three space dimensions, The constant c , {\displaystyle c,} the speed of light, converts time t {\displaystyle t} units (like seconds) into space units (like meters). The squared interval Δ s 2 {\displaystyle \Delta s^{2}}

8140-455: The distance Δ d {\displaystyle \Delta {d}} between two points can be defined using the Pythagorean theorem : Although two viewers may measure the x , y , and z position of the two points using different coordinate systems, the distance between the points will be the same for both, assuming that they are measuring using the same units. The distance

8288-664: The LIGO Scientific Collaboration and the Virgo collaboration announced the first direct detection of gravitational waves , representing the first observation of a black hole merger. On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope (EHT) in 2017 of the supermassive black hole in Messier 87's galactic centre . As of 2023,

8436-481: The Oppenheimer–Snyder model in their paper "On Continued Gravitational Contraction", which predicted the existence of black holes. In the paper, which made no reference to Einstein's recent publication, Oppenheimer and Snyder used Einstein's own theory of general relativity to show the conditions on how a black hole could develop, for the first time in contemporary physics. In 1958, David Finkelstein identified

8584-429: The ct ′ axis is tilted with respect to the ct axis by an angle θ given by The x ′ axis is also tilted with respect to the x axis. To determine the angle of this tilt, we recall that the slope of the world line of a light pulse is always ±1. Fig. 2-3c presents a spacetime diagram from the viewpoint of observer O′. Event P represents the emission of a light pulse at x ′ = 0, ct ′ = −

8732-587: The data reduction following an experiment, the time when a signal is received will be corrected to reflect its actual time were it to have been recorded by an idealized lattice of clocks. In many books on special relativity, especially older ones, the word "observer" is used in the more ordinary sense of the word. It is usually clear from context which meaning has been adopted. Physicists distinguish between what one measures or observes , after one has factored out signal propagation delays, versus what one visually sees without such corrections. Failing to understand

8880-487: The ergosurface , which coincides with the event horizon at the poles but is at a much greater distance around the equator. Objects and radiation can escape normally from the ergosphere. Through the Penrose process , objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole. Thereby the rotation of the black hole slows down. A variation of

9028-512: The geodesic that light travels on never leaves the surface of the "star" (black hole). In 1915, Albert Einstein developed his theory of general relativity , having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations that describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste ,

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9176-408: The gravitational constant and let M be the mass of the earth (or other gravitating body) and m be the mass of the escaping body or projectile. At a distance r from the centre of gravitation the body feels an attractive force The work needed to move the body over a small distance dr against this force is therefore given by The total work needed to move the body from the surface r 0 of

9324-431: The gravitational sphere of influence of a given body. For example, in solar system exploration it is useful to know whether a probe will continue to orbit the Earth or escape to a heliocentric orbit . It is also useful to know how much a probe will need to slow down in order to be gravitationally captured by its destination body. Rockets do not have to reach escape velocity in a single maneuver, and objects can also use

9472-399: The x and ct axes. Since OP = OQ = OR, the angle between x ′ and x must also be θ . Escape velocity In celestial mechanics , escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body , assuming: Although the term escape velocity is common, it is more accurately described as

9620-557: The "noodle effect". In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole . The possibility of travelling to another universe is, however, only theoretical since any perturbation would destroy this possibility. It also appears to be possible to follow closed timelike curves (returning to one's own past) around

9768-409: The 'relative to the other' escape velocity becomes : v r − v p = 2 G ( m + M ) d ≈ 2 G M d {\displaystyle v_{r}-v_{p}={\sqrt {\frac {2G(m+M)}{d}}}\approx {\sqrt {\frac {2GM}{d}}}} . Ignoring all factors other than the gravitational force between the body and

9916-430: The 18th century by John Michell and Pierre-Simon Laplace . In 1916, Karl Schwarzschild found the first modern solution of general relativity that would characterise a black hole. Due to his influential research, the Schwarzschild metric is named after him. David Finkelstein , in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. Black holes were long considered

10064-531: The 2020 Nobel Prize in Physics , Hawking having died in 2018. Based on observations in Greenwich and Toronto in the early 1970s, Cygnus X-1 , a galactic X-ray source discovered in 1964, became the first astronomical object commonly accepted to be a black hole. Work by James Bardeen , Jacob Bekenstein , Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics . These laws describe

10212-519: The French Guiana Space Centre (latitude 5°14′ N). In most situations it is impractical to achieve escape velocity almost instantly, because of the acceleration implied, and also because if there is an atmosphere, the hypersonic speeds involved (on Earth a speed of 11.2 km/s, or 40,320 km/h) would cause most objects to burn up due to aerodynamic heating or be torn apart by atmospheric drag . For an actual escape orbit,

10360-572: The ISCO), for which any infinitesimal inward perturbations to a circular orbit will lead to spiraling into the black hole, and any outward perturbations will, depending on the energy, result in spiraling in, stably orbiting between apastron and periastron, or escaping to infinity. The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is: and decreases with increasing black hole spin for particles orbiting in

10508-472: The Kerr singularity, which leads to problems with causality like the grandfather paradox . It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes. The appearance of singularities in general relativity is commonly perceived as signalling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to

10656-580: The Lorentz group are closely connected to certain types of sphere , hyperbolic , or conformal geometries and their transformation groups already developed in the 19th century, in which invariant intervals analogous to the spacetime interval are used. Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907,

10804-533: The Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei . In Newtonian gravity , test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called

10952-499: The Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction". This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal , who

11100-462: The behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy , and surface gravity to temperature . The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation . On 11 February 2016,

11248-435: The best suited to the description of our world". Even as late as 1909, Poincaré continued to describe the dynamical interpretation of the Lorentz transform. In 1905, Albert Einstein analyzed special relativity in terms of kinematics (the study of moving bodies without reference to forces) rather than dynamics. His results were mathematically equivalent to those of Lorentz and Poincaré. He obtained them by recognizing that

11396-495: The black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number . This behaviour is so puzzling that it has been called the black hole information loss paradox . The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916. According to Birkhoff's theorem , it

11544-408: The body is: where r is the distance between the center of the body and the point at which escape velocity is being calculated and g is the gravitational acceleration at that distance (i.e., the surface gravity ). For a body with a spherically symmetric distribution of mass, the escape velocity v e {\displaystyle v_{e}} from the surface is proportional to

11692-481: The centre of the planet or moon (that is, not relative to its moving surface). In the right-hand half, V e refers to the speed relative to the central body (for example the sun), whereas V te is the speed (at the visible surface of the smaller body) relative to the smaller body (planet or moon). The last two columns will depend precisely where in orbit escape velocity is reached, as the orbits are not exactly circular (particularly Mercury and Pluto). Let G be

11840-528: The collapse. They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star , which is itself stable. In 1939, Robert Oppenheimer and others predicted that neutron stars above another limit, the Tolman–Oppenheimer–Volkoff limit , would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics

11988-404: The details of the photon orbit, which can be prograde (the photon rotates in the same sense of the black hole spin) or retrograde. Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging ; general relativity predicts that any rotating mass will tend to slightly "drag" along

12136-446: The difference between what one measures and what one sees is the source of much confusion among students of relativity. By the mid-1800s, various experiments such as the observation of the Arago spot and differential measurements of the speed of light in air versus water were considered to have proven the wave nature of light as opposed to a corpuscular theory . Propagation of waves

12284-414: The direction at the point of acceleration. If the body accelerates to beyond escape velocity the eventual direction of travel will be at a smaller angle, and indicated by one of the asymptotes of the hyperbolic trajectory it is now taking. This means the timing of the acceleration is critical if the intention is to escape in a particular direction. If the speed at periapsis is v , then the eccentricity of

12432-446: The discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole . Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged . Through

12580-457: The distance between the two events (because of length contraction ). Special relativity provides a new invariant, called the spacetime interval , which combines distances in space and in time. All observers who measure the time and distance between any two events will end up computing the same spacetime interval. Suppose an observer measures two events as being separated in time by Δ t {\displaystyle \Delta t} and

12728-407: The end of their life cycle. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of solar masses ( M ☉ ) may form by absorbing other stars and merging with other black holes, or via direct collapse of gas clouds . There is consensus that supermassive black holes exist in the centres of most galaxies . The presence of

12876-472: The energy required to escape the Earth's gravitational field is GMm / r , a function of the object's mass (where r is radius of the Earth , nominally 6,371 kilometres (3,959 mi), G is the gravitational constant , and M is the mass of the Earth , M = 5.9736 × 10 kg ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by

13024-422: The entire theory can be built upon two postulates: the principle of relativity and the principle of the constancy of light speed. His work was filled with vivid imagery involving the exchange of light signals between clocks in motion, careful measurements of the lengths of moving rods, and other such examples. Einstein in 1905 superseded previous attempts of an electromagnetic mass –energy relation by introducing

13172-535: The escape speed v e , {\displaystyle v_{e},} the object will asymptotically approach the hyperbolic excess speed v ∞ , {\displaystyle v_{\infty },} satisfying the equation: For example, with the definitional value for standard gravity of 9.80665 m/s (32.1740 ft/s ), the escape velocity is 11.186 km/s (40,270 km/h; 25,020 mph; 36,700 ft/s). For an object of mass m {\displaystyle m}

13320-439: The event horizon of a black hole at equilibrium is always spherical. For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate. At the centre of a black hole, as described by general relativity, may lie a gravitational singularity , a region where the spacetime curvature becomes infinite. For a non-rotating black hole, this region takes

13468-421: The event horizon. While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon. For a Kerr black hole the radius of the photon sphere depends on the spin parameter and on

13616-438: The extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity . It is generally expected that such a theory will not feature any singularities. The photon sphere is a spherical boundary where photons that move on tangents to that sphere would be trapped in

13764-611: The fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe that is noticeably different from what they might observe if the world were Euclidean. It was only with the advent of sensitive scientific measurements in the mid-1800s, such as the Fizeau experiment and the Michelson–Morley experiment , that puzzling discrepancies began to be noted between observation versus predictions based on

13912-556: The further development of general relativity, Einstein fully incorporated the spacetime formalism. When Einstein published in 1905, another of his competitors, his former mathematics professor Hermann Minkowski , had also arrived at most of the basic elements of special relativity. Max Born recounted a meeting he had made with Minkowski, seeking to be Minkowski's student/collaborator: I went to Cologne, met Minkowski and heard his celebrated lecture 'Space and Time' delivered on 2 September 1908. [...] He told me later that it came to him as

14060-497: The general equivalence of mass and energy , which was instrumental for his subsequent formulation of the equivalence principle in 1907, which declares the equivalence of inertial and gravitational mass. By using the mass–energy equivalence, Einstein showed that the gravitational mass of a body is proportional to its energy content, which was one of the early results in developing general relativity . While it would appear that he did not at first think geometrically about spacetime, in

14208-408: The geometric interpretation of relativity proved to be vital. In 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity. Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. In three dimensions,

14356-472: The gravitational field of a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. Imagine that a spaceship of mass m is initially at a distance r from the center of mass of the planet, whose mass is M , and its initial speed is equal to its escape velocity, v e {\displaystyle v_{e}} . At its final state, it will be an infinite distance away from

14504-418: The hypothetical aether on the speed of light, and the most likely explanation, complete aether dragging, was in conflict with the observation of stellar aberration . George Francis FitzGerald in 1889, and Hendrik Lorentz in 1892, independently proposed that material bodies traveling through the fixed aether were physically affected by their passage, contracting in the direction of motion by an amount that

14652-419: The implicit assumption of Euclidean space. In special relativity, an observer will, in most cases, mean a frame of reference from which a set of objects or events is being measured. This usage differs significantly from the ordinary English meaning of the term. Reference frames are inherently nonlocal constructs, and according to this usage of the term, it does not make sense to speak of an observer as having

14800-828: The larger and the smaller mass must be accelerated in the gravitational field. Relative to the center of mass the velocity of the larger mass ( v p {\displaystyle v_{p}} , for planet) can be expressed in terms of the velocity of the smaller mass ( v r {\displaystyle v_{r}} , for rocket). We get v p = − m M v r {\displaystyle v_{p}=-{\frac {m}{M}}v_{r}} . The 'barycentric' escape velocity now becomes : v r = 2 G M 2 d ( M + m ) ≈ 2 G M d {\displaystyle v_{r}={\sqrt {\frac {2GM^{2}}{d(M+m)}}}\approx {\sqrt {\frac {2GM}{d}}}} while

14948-544: The mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. The total electric charge  Q and the total angular momentum  J are expected to satisfy the inequality for a black hole of mass M . Black holes with the minimum possible mass satisfying this inequality are called extremal . Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from

15096-501: The mass. An object has reached escape velocity when the specific orbital energy is greater than or equal to zero. The existence of escape velocity can be thought of as a consequence of conservation of energy and an energy field of finite depth. For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity field) it is only possible for the object to reach combinations of locations and speeds which have that total energy; places which have

15244-438: The math with no loss of generality in the conclusions that are reached. In Fig. 2-2, two Galilean reference frames (i.e. conventional 3-space frames) are displayed in relative motion. Frame S belongs to a first observer O, and frame S′ (pronounced "S prime") belongs to a second observer O′. Fig. 2-3a redraws Fig. 2-2 in a different orientation. Fig. 2-3b illustrates a relativistic spacetime diagram from

15392-412: The microscopic level, because they are time-reversible . Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from

15540-513: The moving surface at the point of launch to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s relative to that moving surface . The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28′ N) and

15688-472: The nearest known body thought to be a black hole, Gaia BH1 , is around 1,560 light-years (480 parsecs ) away. Though only a couple dozen black holes have been found so far in the Milky Way, there are thought to be hundreds of millions, most of which are solitary and do not cause emission of radiation. Therefore, they would only be detectable by gravitational lensing . John Michell used the term "dark star" in

15836-499: The object, an object projected vertically at speed v {\displaystyle v} from the surface of a spherical body with escape velocity v e {\displaystyle v_{e}} and radius R {\displaystyle R} will attain a maximum height h {\displaystyle h} satisfying the equation which, solving for h results in where x = v / v e {\textstyle x=v/v_{e}}

15984-512: The observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. In ordinary space, a position is specified by three numbers, known as dimensions . In the Cartesian coordinate system , these are often called x , y and z . A point in spacetime

16132-430: The other' and the 'barycentric' escape velocities are the same, namely v e = 2 G M d {\displaystyle v_{e}={\sqrt {\frac {2GM}{d}}}} . But when we can't neglect the smaller mass (say m {\displaystyle m} ) we arrive at slightly different formulas. Because the system has to obey the law of conservation of momentum we see that both

16280-408: The other, central body or relative to center of mass or barycenter of the system of bodies. Thus for systems of two bodies, the term escape velocity can be ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. Escape velocity usually refers to the escape velocity of zero mass test particles . For zero mass test particles we have that the 'relative to

16428-423: The outside, and hence are deemed unphysical . The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter . This is supported by numerical simulations. Due to the relatively large strength of the electromagnetic force , black holes forming from the collapse of stars are expected to retain the nearly neutral charge of

16576-467: The physical constituents of matter. Lorentz's equations predicted a quantity that he called local time , with which he could explain the aberration of light , the Fizeau experiment and other phenomena. Henri Poincaré was the first to combine space and time into spacetime. He argued in 1898 that the simultaneity of two events is a matter of convention. In 1900, he recognized that Lorentz's "local time"

16724-404: The planet, and its speed will be negligibly small. Kinetic energy K and gravitational potential energy U g are the only types of energy that we will deal with (we will ignore the drag of the atmosphere), so by the conservation of energy, We can set K final = 0 because final velocity is arbitrarily small, and U g   final = 0 because final gravitational potential energy

16872-486: The postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional spacetime by defining various four vectors , namely four-position , four-velocity , and four-force . He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems

17020-455: The presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole. To a distant observer, clocks near a black hole would appear to tick more slowly than those farther away from the black hole. Due to this effect, known as gravitational time dilation , an object falling into

17168-513: The radius assuming constant density, and proportional to the square root of the average density ρ. where K = 8 3 π G ≈ 2.364 × 10 − 5  m 1.5  kg − 0.5  s − 1 {\textstyle K={\sqrt {{\frac {8}{3}}\pi G}}\approx 2.364\times 10^{-5}{\text{ m}}^{1.5}{\text{ kg}}^{-0.5}{\text{ s}}^{-1}} This escape velocity

17316-530: The same direction as the spin. Spacetime Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity . In 1908, Hermann Minkowski presented

17464-413: The same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics is currently an unsolved problem. These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly,

17612-410: The same. Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula where: The value GM is called the standard gravitational parameter , or μ , and is often known more accurately than either G or M separately. When given an initial speed V {\displaystyle V} greater than

17760-479: The shape of a single point; for a rotating black hole it is smeared out to form a ring singularity that lies in the plane of rotation. In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density . Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into

17908-477: The shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behaviour of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance —the membrane paradigm . This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at

18056-404: The singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky , Isaak Khalatnikov , and Evgeny Lifshitz , who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically. For this work, Penrose received half of

18204-505: The singularity disappeared after a change of coordinates. In 1933, Georges Lemaître realised that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity . Arthur Eddington commented on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high

18352-419: The singularity once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a limit. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or

18500-409: The spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. The ergosphere of a black hole is a volume bounded by the black hole's event horizon and

18648-733: The spacetime interval d s ′ {\displaystyle ds'} can be written in a same form as above. Because of the constancy of speed of light, the light events in all inertial frames belong to zero interval, d s = d s ′ = 0 {\displaystyle ds=ds'=0} . For any other infinitesimal event where d s ≠ 0 {\displaystyle ds\neq 0} , one can prove that d s 2 = d s ′ 2 {\displaystyle ds^{2}=ds'^{2}} which in turn upon integration leads to s = s ′ {\displaystyle s=s'} . The invariance of

18796-584: The spacetime interval between the same events for all inertial frames of reference is one of the fundamental results of special theory of relativity. Although for brevity, one frequently sees interval expressions expressed without deltas, including in most of the following discussion, it should be understood that in general, x {\displaystyle x} means Δ x {\displaystyle \Delta {x}} , etc. We are always concerned with differences of spatial or temporal coordinate values belonging to two events, and since there

18944-416: The spacetime interval between two events on the world line of something moving at the speed of light is zero. Such an interval is termed lightlike or null . A photon arriving in our eye from a distant star will not have aged, despite having (from our perspective) spent years in its passage. A spacetime diagram is typically drawn with only a single space and a single time coordinate. Fig. 2-1 presents

19092-436: The speed of light, their world lines have a slope of ±1. In other words, every meter that a photon travels to the left or right requires approximately 3.3 nanoseconds of time. To gain insight in how spacetime coordinates measured by observers in different reference frames compare with each other, it is useful to work with a simplified setup with frames in a standard configuration. With care, this allows simplification of

19240-504: The star, leaving us outside (i.e., nowhere)." In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4  M ☉ ) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau , who argued that some yet unknown mechanism would stop

19388-433: The star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105 appears to have an angular momentum near the maximum allowed value. That uncharged limit is allowing definition of a dimensionless spin parameter such that Black holes are commonly classified according to their mass, independent of angular momentum, J . The size of

19536-402: The state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and David Hilbert led an advanced seminar attended by notable physicists of the time to study the papers of Lorentz, Poincaré et al. Minkowski saw Einstein's work as an extension of Lorentz's, and was most directly influenced by Poincaré. On 5 November 1907 (a little more than

19684-426: The surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius. Also in 1939, Einstein attempted to prove that black holes were impossible in his publication "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses", using his theory of general relativity to defend his argument. Months later, Oppenheimer and his student Hartland Snyder provided

19832-430: The term for its brevity and "advertising value", and it quickly caught on, leading some to credit Wheeler with coining the phrase. The no-hair theorem postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share

19980-516: The total mass inside a sphere containing a black hole can be found by using the gravitational analogue of Gauss's law (through the ADM mass ), far away from the black hole. Likewise, the angular momentum (or spin) can be measured from far away using frame dragging by the gravitomagnetic field , through for example the Lense–Thirring effect . When an object falls into a black hole, any information about

20128-478: The trajectory is given by: This is valid for elliptical, parabolic, and hyperbolic trajectories. If the trajectory is hyperbolic or parabolic, it will asymptotically approach an angle θ {\displaystyle \theta } from the direction at periapsis, with The speed will asymptotically approach In this table, the left-hand half gives the escape velocity from the visible surface (which may be gaseous as with Jupiter for example), relative to

20276-432: The usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. Scholars of the time were initially excited by the proposal that giant but invisible 'dark stars' might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century, as if light were

20424-417: The velocity equation in circular orbit ). This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential and kinetic energy needs to be at least zero. The velocity corresponding to the circular orbit is sometimes called the first cosmic velocity , whereas in this context the escape velocity

20572-427: The velocity of an object traveling under the gravitational influence of the primary. If an object is in a circular or elliptical orbit, its speed is always less than the escape speed at its current distance. In contrast if it is on a hyperbolic trajectory its speed will always be higher than the escape speed at its current distance. (It will slow down as it gets to greater distance, but do so asymptotically approaching

20720-447: The viewpoint of observer O. Since S and S′ are in standard configuration, their origins coincide at times t  = 0 in frame S and t ′ = 0 in frame S′. The ct ′ axis passes through the events in frame S′ which have x ′ = 0. But the points with x ′ = 0 are moving in the x -direction of frame S with velocity v , so that they are not coincident with the ct axis at any time other than zero. Therefore,

20868-406: The whole ensemble of clocks associated with one inertial frame of reference. In this idealized case, every point in space has a clock associated with it, and thus the clocks register each event instantly, with no time delay between an event and its recording. A real observer, will see a delay between the emission of a signal and its detection due to the speed of light. To synchronize the clocks, in

21016-479: The work of Werner Israel , Brandon Carter , and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric : mass , angular momentum , and electric charge. At first, it was suspected that the strange features of the black hole solutions were pathological artefacts from the symmetry conditions imposed, and that

21164-555: Was exactly what was necessary to explain the negative results of the Michelson–Morley experiment. No length changes occur in directions transverse to the direction of motion. By 1904, Lorentz had expanded his theory such that he had arrived at equations formally identical with those that Einstein was to derive later, i.e. the Lorentz transformation . As a theory of dynamics (the study of forces and torques and their effect on motion), his theory assumed actual physical deformations of

21312-536: Was less than the sum of the speed of light in air plus the speed of the water by an amount dependent on the water's index of refraction. Among other issues, the dependence of the partial aether-dragging implied by this experiment on the index of refraction (which is dependent on wavelength) led to the unpalatable conclusion that aether simultaneously flows at different speeds for different colors of light. The Michelson–Morley experiment of 1887 (Fig. 1-2) showed no differential influence of Earth's motions through

21460-477: Was likely to intervene and stop at least some stars from collapsing to black holes. Their original calculations, based on the Pauli exclusion principle , gave it as 0.7  M ☉ . Subsequent consideration of neutron-neutron repulsion mediated by the strong force raised the estimate to approximately 1.5  M ☉ to 3.0  M ☉ . Observations of the neutron star merger GW170817 , which

21608-414: Was then assumed to require the existence of a waving medium; in the case of light waves, this was considered to be a hypothetical luminiferous aether . The various attempts to establish the properties of this hypothetical medium yielded contradictory results. For example, the Fizeau experiment of 1851, conducted by French physicist Hippolyte Fizeau , demonstrated that the speed of light in flowing water

21756-457: Was urged to publish it. These results came at the beginning of the golden age of general relativity , which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967, which, by 1969, were shown to be rapidly rotating neutron stars. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but

21904-628: Was used in print by Life and Science News magazines in 1963, and by science journalist Ann Ewing in her article " 'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio. In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler ; Wheeler adopted

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