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General relativity
In 1915, Albert Einstein developed his general theory of relativity, having earlier shown that gravity does influence light's motion. A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[5] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood then and Schwarzschild himself thought it was not physical. Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.
In 1930, astrophysicist Subrahmanyan Chandrasekhar calculated, using general relativity, that a non-rotating body of electron-degenerate matter above 1.44 solar masses (the Chandrasekhar limit) would collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle. But in 1939, Robert Oppenheimer and others predicted that stars above approximately three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[6]
Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words some of the terms in the equations became infinite at the Schwarzschild radius. This was interpreted as indicating that the Schwarzschild radius 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. Because of this property, the collapsed stars were called "frozen stars,"[7] because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. This is a known property of modern black holes, but it must be emphasized that the light from the surface of the frozen star becomes redshifted very fast, turning the black hole black very quickly. Many physicists could not accept the idea of time standing still at the Schwarzschild radius, and there was little interest in the subject for over 20 years.
Golden age
See also: golden age of general relativity
In 1958, David Finkelstein introduced the concept of the event horizon by presenting Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2m [in geometrized units, i.e. 2Gm/c2] is not a singularity, but that it acts as a perfect unidirectional membrane: causal influences can cross it in only one direction".[8] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. All theories up to this point, including Finkelstein's, covered only non-rotating black holes. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Roger Penrose was able to prove that singularities occur inside any black hole.[9] In 1967, astronomers discovered pulsars,[10][11] and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.
The term "black hole" was first publicly used by John Wheeler during a lecture in 1967. Although he is usually credited with coining the phrase, he always insisted that it was suggested to him by somebody else. The first recorded use of the term is in a 1964 letter by Anne Ewing to the AAAS.[12] After Wheeler's use of the term, it was quickly adopted in general use. However, the term itself has been controversial among some.
Properties and structure
The no hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum.[13] Any two black holes that share the same values for these properties, or parameters, are classically indistinguishable.
These properties are special because they are visible from outside the black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.[14] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
When an object falls into a black hole, any information about 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 behavior of the horizon in this situation is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance, a dissipative system (see membrane paradigm).[15] This is different from other field theories like electromagnetism, which does not have any friction or resistivity at the microscopic level, because they are time reversible. Because the 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 the 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 the black hole horizon, including the total baryon number, lepton number, and all the other nearly conserved pseudo-charges of particle physics. This behavior is so puzzling, that it has been called the black hole information loss paradox.[16][17][18]
Physical properties
The simplest black hole has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.[5] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[19] This means that there is no observable difference 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 only correct near the black hole horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[20]
Solutions describing more general black holes also exist. Charged black holes are desribed by the Reissner-Nordström metric, while the Kerr metric describes a 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 the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In natural units, the total charge Q and the total angular momentum J are expected to satisfy
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