Counting Schwarzschild and Charged Black Holes

TL;DR

The paper investigates whether fundamental string states correspond one-to-one with black hole states, using Schwarzschild and highly non-extremal charged black holes as test cases. It develops a strategy to relate string-level degeneracy to black hole entropy by matching low-energy string observables, such as the absorption cross section and Hawking luminosity, to the classical horizon area, and derives that $A_H=4G_N S\sqrt{36/(c_L c_R)}$. The key finding is that area and entropy are proportional only if $c_L=c_R$, and exact Bekenstein--Hawking matching requires $c=6$, a value not realized in known string theories, suggesting possible nonperturbative renormalization effects near horizons. The approach is extended to charged, rotating, and higher-dimensional black holes, showing the method’s applicability beyond near-extremality and highlighting its potential implications for understanding black hole microstates in string theory.

Abstract

We review the arguments that fundamental string states are in one to one correspondence with black hole states. We demonstrate the power of the assumption by showing that it implies that the statistical entropy of a wide class of nonextreme black holes occurring in string theory is proportional to the horizon area. However, the numerical coefficient relating the area and entropy only agrees with the Bekenstein--Hawking formula if the central charge of the string is six which does not correspond to any known string theory. Unlike the current D-brane methods the method used in this paper is applicable for the case of Schwarzschild and highly non-extreme charged black holes.