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In equations, Hawking showed that if one denotes the creation and annihilation operators at a frequency for a quantum field propagating in the black-hole background by and † then the expectation value of the product of these operators in the state formed by the collapse of a black hole would satisfy † = / where k is the Boltzmann constant ...
A singularity in solutions of the Einstein field equations is one of three things: Spacelike singularities: The singularity lies in the future or past of all events within a certain region. The Big Bang singularity and the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike.
A black hole with the mass of a car would have a diameter of about 10 −24 m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c 2 would take less than 10 −88 ...
A black hole cosmology (also called Schwarzschild cosmology or black hole cosmological model) is a cosmological model in which the observable universe is the interior of a black hole. Such models were originally proposed by theoretical physicist Raj Kumar Pathria , [ 1 ] and concurrently by mathematician I. J. Good .
Because this particle has angular momentum, it can only be captured by the black hole if the maximum potential of the black hole is less than () /. Solving the above effective potential equation for the maximum under the given conditions results in a maximum potential of exactly ( e 2 − 1 ) / 2 {\displaystyle (e^{2}-1)/2} .
Modern black holes were first predicted by Einstein's 1915 theory of general relativity.Evidence of the astrophysical objects termed black holes began to mount half a century later, [3] and these objects are of current interest primarily because of their compact size and immense gravitational attraction.
Scientists studying the earliest black holes may have found an answer to dark matter, putting Stephen Hawking’s theory on the subject back into the spotlight.
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.