Black Holes and D-Branes

Abstract

Under a wide variety of conditions General Relativity predicts that singularities will develop [1]. The cosmic censorship hypothesis states that under generic physical situations leading to gravitational collapse the resulting singularities will be covered by an event horizon [2]. This conjecture has not been yet proved but there exists great evidence that it is correct [3]. The area of the horizon is an interesting quantity since it always increases upon classical evolution [4], this looks very similar to the second law of thermodynamics. The analogy became more precise when Hawking showed [5] that quantum mechanics implies that black holes emit thermal radiation with a temperature obeying the first law of thermodynamics dM = T _H dS, where the entropy is $S = {{{A_H}} \over {4{G_N}\hbar }}$ [6], M is the black hole mass and A _H is the horizon area (from now on we set ħ = 1 but keep G _N ≠ 1). The area increase law becomes the second law of thermodynamics. If one includes Hawking radiation, the black hole mass decreases and so does the area of the horizon, but the total entropy, defined as S = A _H /4G _N + S _rad , increases. For any physical system we expect that the entropy is the logarithm of the number of states with given macroscopic properties, like the mass, charge, angular momentum, etc. It has been a longstanding puzzle to find the degrees of freedom that give rise to this entropy. It seems clear that some quantum gravity will be necessary to describe the microstates. String theory [7] is a theory of quantum gravity so one would naturally expect that it should give an answer to this question. But string theory is defined perturbatively and black holes involve strong interactions due to their large mass.