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The black hole entropy is proportional to the area of its event horizon . The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle. [2]
According to the Bekenstein bound, the entropy of a black hole is proportional to the number of Planck areas that it would take to cover the black hole's event horizon.. In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of ...
The entropy of a black hole is proportional to the surface area of the black hole's event horizon. [ 92 ] [ 93 ] [ 94 ] Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size.
In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. He wrote that a black hole's entropy was proportional to the area of its (the black hole's) event horizon. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems including black holes.
when E c =E, which is the Bekenstein bound. The Cardy–Verlinde formula was later shown by Kutasov and Larsen [4] to be invalid for weakly interacting CFTs. In fact, since the entropy of higher dimensional (meaning n>1) CFTs is dependent on exactly marginal couplings, it is believed that a Cardy formula for the entropy is not achievable when n>1.
The thermodynamic description of gravity has a history that goes back at least to research on black hole thermodynamics by Bekenstein and Hawking in the mid-1970s. These studies suggest a deep connection between gravity and thermodynamics, which describes the behavior of heat.
Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be somehow encoded onto a bounding surface.
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 ...