On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

TL;DR

This review explores the deep connections between black hole thermodynamics, spacetime singularities, and gravitational entropy, questioning fundamental assumptions and proposing new perspectives on black hole microstructures and the role of singularities.

Contribution

It offers a comprehensive examination of singularities in quantum gravity, defines gravitational entropy via curvature invariants, and introduces the Hookean law for black holes, linking thermodynamics with microstructure insights.

Findings

Black hole entropy varies across theories, reflecting different microstructures.

The Hookean law relates black hole fragmentation to thermodynamic forces.

Spacetime singularities may persist in quantum gravity, affecting thermodynamic interpretations.

Abstract

Many fundamental issues remain for black hole thermodynamics after almost half a century of its conception. For example, what are the underlying degrees of freedom of a black hole horizon that give rise to said thermodynamical properties? Furthermore, classical black holes also harbor a spacetime singularity. Although it is often believed that quantum gravity would "cure" the singularity, as emphasized by Penrose, this viewpoint requires a deeper examination. In this review, I will examine the possibility that singularities remain in quantum gravity, the roles they may play, and the possible links between singularity and black hole thermodynamics. I will also discuss how -- inspired by Penrose's Weyl curvature hypothesis -- gravitational entropy for a black hole can be defined using curvature invariants, and the surprising implication that the entropy of black holes in different theories of gravity are different manifestations of spacetime curvature, i.e., their underlying microstructures could be different. Finally, I review the "Hookean law" recently established for singly rotating Myers-Perry black holes (including Kerr black holes) that connect black hole fragmentation -- a consequence of the second law of black hole thermodynamics -- with the maximum "Hookean force", as well as with the thermodynamic geometry of Ruppeiner. This also suggests a new way to study black hole microstructures, and hints at the possibility that some black holes are beyond the Hookean regime (and thus have different microstructures). While examining the remarkable connections between black hole thermodynamics, spacetime singularities and cosmic censorship, as well as gravitational entropy, I shall point out some subtleties, provide some new thoughts, and raise some hard but fundamental questions, including whether black hole thermodynamics is really just "ordinary thermodynamics" or something quite different.