Black hole

A black hole is an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. In general relativity, a black hole's event horizon seals an object's fate but produces no locally detectable change when crossed. General relativity also predicts that every black hole should have a central singularity, where the curvature of spacetime is infinite.

In many ways, 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 the 18th century. In 1916, the first solution of general relativity that would characterise a black hole was found. By the late 1950s, this solution began to be interpreted physically as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The first black hole known was Cygnus X-1, identified by several researchers independently in 1971.

Black holes typically form when massive stars collapse at 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 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 a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter falling toward a black hole can form an accretion disk of infalling plasma, heated by friction and emitting light. In extreme cases, this creates a quasar, some of the brightest objects in the universe. Merging black holes can also be detected by observation of the gravitational waves they emit. If other stars are orbiting 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.

History

The idea of a body so massive that even light could not escape was first proposed in the late 18th century by English astronomer 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 hypothesized 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 Exposition du Système du Monde. Franz Xaver von Zach asked Laplace for a mathematical analysis, which Laplace provided and published in a journal edited by von Zach.

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. In 1907, Einstein published a paper proposing his equivalence principle, the hypothesis that inertial mass and gravitational mass have a common cause. Using the principle, Einstein predicted the redshift and half of the lensing effect of gravity on light; the full prediction of gravitational lensing required development of general relativity.

By 1915, 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 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. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution. 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 sceptical of the existence of black holes. In a 1926 popular science book, Arthur Eddington critiqued the idea of a star with mass compressed to its Schwarzschild radius as a flaw in the then-poorly-understood theory of general relativity. 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, Subrahmanyan Chandrasekhar calculated that a non-rotating body of electron-degenerate matter below a certain limiting mass is stable, and by 1934 he showed that this explained the catalogue of white dwarf stars. When 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.

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 1939, based on Chandrasekhar's reasoning, J. Robert Oppenheimer and George Volkoff predicted that neutron stars below a certain mass limit, later called 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 through electron degeneracy and 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.

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 idealised 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. However, as the density of the star increases, gravitational time dilation increases and the collapse, viewed from afar, seems to slow down further and further until the star reaches its Schwarzschild radius, where it appears frozen in time.