Black hole entropy
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Black hole entropy is entropy carried by a black hole.
If black hole carried no entropy, it would be possible to violate the second law of thermodynamics by throwing mass into the black hole. The only way to satisfy the second law is to admit that the black holes have entropy whose increase more-than-compensates the decrease of the entropy carried by the object that was swallowed.
Starting from some theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon. Later, Stephen Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain temperature (Hawking temperature). Using some arguments rooted in thermodynamics, Hawking was also able to calculate the entropy that the black hole must carry. The result confirmed Bekenstein's conjecture:
- <math>S_{BH} = k_{\mathrm{Boltzmann}} \frac{A}{l_{\mathrm{Planck}}^2}<math>
where <math>k_{\mathrm{Boltzmann}}<math> is Boltzmann's constant, and <math>l_{\mathrm{Planck}}=\sqrt{G\hbar / c^3}<math> is the Planck length. The black hole entropy is proportional to its area <math>A<math>. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".
Until 1995, no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, i.e. on counting the number of actual microstates. The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes. Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
Loop quantum gravity, viewed as the main competitor of string theory, also offered a slightly more heuristic calculation of the black hole entropy. Unfortunately, the numerical coefficient <math>1/4<math> was not reproduced correctly. The multiplicative discrepancy is called the Immirzi parameter.Template:Physics-stub