Lectures on Quantum Black Holes

TL;DR

This paper reviews recent advances in understanding finite size corrections to black hole entropy, highlighting progress in string theory and the detailed microscopic information these corrections reveal.

Contribution

It discusses new methods for calculating finite size effects in quantum black holes, extending beyond the large charge approximation.

Findings

Finite size corrections depend on the phase of the black hole.

Nonperturbative effects can be explored and match thermodynamic predictions.

Corrections provide insights into the microscopic structure of quantum black holes.

Abstract

In these notes we describe recent progress in understanding finite size corrections to the black hole entropy. Much of the earlier work concerning quantum black holes has been in the limit of large charges when the area of the even horizon is also large. In recent years there has been substantial progress in understanding the entropy of supersymmetric black holes within string theory going well beyond the large charge limit. It has now become possible to begin exploring finite size effects in perturbation theory in inverse size and even nonperturbatively, with highly nontrivial agreements between thermodynamics and statistical mechanics. Unlike the leading Bekenstein-Hawking entropy which follows from the two-derivative Einstein-Hilbert action, these finite size corrections depend sensitively on the phase under consideration and contain a wealth of information about the details of compactification as well as the spectrum of nonperturbative states in the theory. Finite-size corrections are therefore very interesting as a valuable window into the microscopic degrees of freedom of the quantum theory.