The entropy of black holes: a primer

TL;DR

This paper reviews the thermodynamics and entropy of black holes, discussing classical and quantum perspectives, including string theory approaches to microstate counting and the correspondence between string states and black holes.

Contribution

It provides a comprehensive overview of black hole entropy, emphasizing recent string theory results and the connection between quantum microstates and macroscopic black hole properties.

Findings

Black hole entropy relates to quantum microstates.

String theory offers methods to count microstates.

Connections between string states and black holes are explored.

Abstract

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiation spectrum of a black hole, involving a thermal (Planckian) factor. One then discusses the attempts to interpret the black-hole entropy as the logarithm of the number of quantum micro-states of a macroscopic black hole, with particular emphasis on results obtained within string theory. After mentioning the (technically cleaner, but conceptually more intricate) case of supersymmetric (BPS) black holes and the corresponding counting of the degeneracy of Dirichlet-brane systems, one discusses in some detail the ``correspondence'' between massive string states and non-supersymmetric Schwarzschild black holes.