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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]
In physics, the Cardy formula gives the entropy of a two-dimensional conformal field theory (CFT). In recent years, this formula has been especially useful in the calculation of the entropy of BTZ black holes and in checking the AdS/CFT correspondence and the holographic principle.
The Bekenstein-Hawking entropy of a black hole is proportional to the surface area of the black hole as expressed in Planck units. Information content is defined as the logarithm of the reciprocal of the probability that a system is in a specific microstate, and the information entropy of a system is the expected value of the system's ...
Although general relativity can be used to perform a semiclassical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities, such as mass, charge, pressure, etc ...
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.
Early research into black holes was done by individuals such as Karl Schwarzschild and John Wheeler, who modeled black holes as having zero entropy. [3] [4] A black hole can form when enough matter or energy is compressed into a volume small enough that the escape velocity is greater than the speed of light. Because nothing can travel that fast ...
Such black holes are stable and emit no Hawking radiation. Their black hole entropy [2] can be calculated in string theory. It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero. Carroll explains the lack of entropy by creating a separate dimension for the black hole to exist within. [3]
However, this concept demonstrates that black holes radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore temperature. The loss of energy also implies that black holes do not last forever, but rather evaporate or decay slowly.