Black holes have primarily been subjects of research since the advent of general relativity in the early 1900s, although similar concepts were discussed before then. Several months after Albert Einstein first described general relativity in 1917, astrophysicist Karl Schwarzschild applied the model to stars and discovered a solution to the Einstein field equations containing singularities, which would later become known as the Schwarzschild solution. This solution was the foundation for Schwarzschild black holes: black holes with no spin or charge.
Initially, black holes were dismissed by early researchers as purely theoretical curiosities or even physically impossible. The emerging concept of degeneracy pressure led many physicists to believe that a yet-to-be-known mechanism would stop a star from collapsing into a black hole, no matter its mass. However, in 1939, J. Robert Oppenheimer and Hartland Snyder analyzed stellar collapse and determined that there seemed to be no mechanism that could prevent all stars from becoming black holes.
After Oppenheimer's and Snyder's discovery, black holes began to become more widely accepted among physicists, who began to further investigate and understand the Schwarzschild solution. Three more metrics were created to describe other kinds of black holes: the Reissner-Nordstrom metric, describing charged, nonspinning black holes, the Kerr metric, describing spinning, uncharged black holes, and the Kerr-Newman metric, describing spinning and charged black holes. Werner Israel later discovered that any black hole must be described by one of these parameters and can only have three properties: charge, mass, and spin.
Meanwhile, actual astronomical observations of black holes were beginning. The first widely recognized black hole, Cygnus X-1, was discovered in 1972 and accepted by most of the scientific community as a black hole by the end of 1973. Although Cygnus X-1 was a stellar black hole, evidence built for the existence of supermassive black holes as well, and the Hubble Space Telescope revealed that supermassive black holes were nearly ubiquitous in galactic centers. In more recent years, advances in interferometry have allowed scientists to take the first photo of a black hole and detect black hole mergers via gravitational waves.
Before general relativity The idea of a body so massive that even light could not escape was briefly proposed by English astronomical pioneer and clergyman John Michell and independently by French scientist Pierre-Simon Laplace. Both scholars proposed very large stars in contrast to the modern concept of an extremely dense object.
Michell's idea, in a short part of a letter published in 1784, calculated that a star with the same density but 500 times the radius of the sun would not let any emitted light escape; the surface escape velocity would exceed the speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.
In 1796, Laplace mentioned that a star could be invisible if it were sufficiently large while speculating on the origin of the Solar System in his book . Franz Xaver von Zach asked Laplace for a mathematical analysis, which Laplace provided and published in a journal edited by von Zach. Laplace omitted his comment about invisible stars in later editions of his book, perhaps because Thomas Young's wave theory of light had cast doubt on the validity of the corpuscles of light used in Laplace's mathematical analysis.
General relativity
In 1905, Albert Einstein showed that the laws of electromagnetism would be invariant under a Lorentz transformation: they would be identical for observers travelling at different velocities relative to each other. This discovery became known as the principle of special relativity. Although the laws of mechanics had already been shown to be invariant, gravity remained yet to be included. To add gravity to his theory of relativity, Einstein was guided by observations by Galileo Galilei, Isaac Newton and others which showed inertial mass equalled gravitational mass. In 1907, Einstein published a paper proposing his equivalence principle, the hypothesis that this equality means the two forms of mass have a common cause. Using the principle, Einstein predicted the redshift effect of gravity on light.
In 1911, Einstein predicted (also in Collected Papers Vol. 3, document 23) the deflection of light by massive bodies, but his analysis was premature and off by a factor of two.
By 1917, Einstein refined these ideas into his general theory of relativity, which explained how matter affects spacetime, which in turn affects the motion of other matter. This theory formed the basis for black hole physics.
Singular solutions in general relativity Only a few months after Einstein published the field equations describing general relativity, astrophysicist Karl Schwarzschild set out to apply the idea to stars. He assumed spherical symmetry with no spin and found a solution to Einstein's equations. Translation: and Translation: A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass using a different set of coordinates. At a certain radius from the center of the mass, the Schwarzschild solution became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this radius, which later became known as the Schwarzschild radius, was not understood at the time.
Many physicists of the early 20th century were skeptical of the existence of black holes. In a 1926 popular science book, Arthur Eddington discussed the idea of a star with mass compressed to its Schwarzschild radius, but his analysis was meant to illustrate issues in the then-poorly-understood theory of general relativity rather than to seriously analyze the problem: Eddington did not believe black holes existed. In 1939, Einstein himself used his theory of general relativity in an attempt to prove that black holes were impossible. His work relied on increasing pressure or increasing centrifugal force balancing the force of gravity so that the object would not collapse beyond its Schwarzschild radius. He missed the possibility that implosion would drive the system below this critical value.
Gravity vs degeneracy pressure By the 1920s, astronomers had classified a number of white dwarf stars as too cool and dense to be explained by the gradual cooling of ordinary stars. In 1926, Ralph Fowler showed that quantum-mechanical degeneracy pressure was larger than thermal pressure at these densities. In 1931, using a combination of special relativity and quantum mechanics, Subrahmanyan Chandrasekhar calculated that a non-rotating body of electron-degenerate matter below a certain limiting mass (now called the Chandrasekhar limit at ) is stable, and by 1934 he showed that this explained the catalog of white dwarf stars. At the same meeting where Chandrasekhar announced his results, Eddington pointed out that stars above this limit would radiate until they were sufficiently dense to prevent light from exiting, a conclusion he considered absurd. Eddington and, later, Lev Landau argued that some yet unknown mechanism would stop the collapse. They were partially correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable. These arguments from senior scientists delayed acceptance of Chandrasekhar's model.
In the 1930s, Fritz Zwicky and Walter Baade studied stellar novae, focusing on exceptionally bright ones they called supernovae. Zwicky promoted the idea that supernovae produced stars with the density of atomic nuclei—neutron stars—but this idea was largely ignored. In 1937, Lev Landau published a detailed model of a nuclear core model for stellar cores, which caught the attention of Robert Oppenheimer. In 1939, based on Chandrasekhar's reasoning, Oppenheimer and George Volkoff predicted that neutron stars below a certain mass limit—now known as the Tolman–Oppenheimer–Volkoff limit—would be stable due to neutron degeneracy pressure. Above that limit, they reasoned that either their model would not apply or that gravitational contraction would not stop.
John Archibald Wheeler and two of his students resolved questions about the model behind the Tolman–Oppenheimer–Volkoff (TOV) limit. Harrison and Wheeler developed the equations of state relating density to pressure for cold matter all the way from atoms through electron degeneracy to neutron degeneracy. Masami Wakano and Wheeler then used the equations to compute the equilibrium curve for stars, relating mass to circumference. They found no additional features that would invalidate the TOV limit. This meant that the only thing that could prevent black holes from forming was a dynamic process ejecting sufficient mass from a star as it cooled. Wheeler held the view that the neutrons in an imploding star would convert to electromagnetic radiation fast enough that the resulting light would not be trapped in a black hole.
Birth of modern model The modern concept of black holes was formulated by Robert Oppenheimer and his student Hartland Snyder in 1939. In the paper, Oppenheimer and Snyder solved Einstein's equations of general relativity for an idealized imploding star, in a model later called the Oppenheimer–Snyder model, then described the results from far outside the star. The implosion starts as one might expect: the star material rapidly collapses inward. But as density of the star increases, gravitational time dilation increases and the collapse, viewed from afar, seems to slow down. Once the star reached a critical radius—its Schwarzschild radius—faraway viewers would no longer see the implosion. The light from the implosion would be infinitely redshifted and time dilation would be so extreme that it would appear frozen in time.
In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, calling it "a perfect unidirectional membrane: causal influences can cross it in only one direction". In this sense, events that occur inside of the black hole cannot affect events that occur outside of the black hole. Finkelstein created a new reference frame 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 similar concept had already been found by Martin Kruskal, but its significance had not been fully understood at the time. Finkelstein's new frame of reference allowed events at the event horizon of an imploding star to be related to events far away. By 1962 the two points of view were reconciled, convincing many skeptics that implosion into a black hole made physical sense.
Golden age
The era from the mid-1960s to the mid-1970s was the "golden age of black hole research", when general relativity and black holes became mainstream subjects of research.
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 cylindrically symmetric solution for a black hole that is both rotating and electrically charged.