Black Hole Entropy and Physics at Planckian Scales

TL;DR

This paper compares various definitions of black hole entropy, highlighting differences between thermodynamical and statistical-mechanical approaches, and discusses the implications of quantum and gravitational effects at Planckian scales.

Contribution

It provides a detailed comparison of entropy definitions and explores the role of the no-boundary wavefunction and renormalization in black hole entropy.

Findings

Thermodynamical and statistical-mechanical entropies do not always coincide.

The no-boundary wavefunction offers insights into the entropy problem.

Renormalization affects the calculation of black hole entropy.

Abstract

We discuss and compare different definitions of the entropy of a black hole. In particular we show that the thermodynamical entropy defined by the response of the free energy of a black hole to the change of temperature does not coincide with the statistical-mechanical entropy, obtained by counting its dynamical degrees of freedom. The no-boundary wavefunction of a black hole, its relation to the entropy problem and its generalization are discussed. We discuss the relation between on-shell and off-shell calculations of the entropy, and the role of the renormalization of the gravitational constant.