On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

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.

An invited contribution to the topical volume [https://link.springer.com/collections/hjjgajaagg] for the conference "Singularity theorems, causality, and all that: A tribute to Roger Penrose" (SCRI21), June 14-18, 2021

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• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• The 1965 Penrose singularity theorem
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• The Measure Problem in Cosmology
• Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind
• Corrected form of the first law of thermodynamics for regular black holes
• Lorentz violation and perpetual motion
• The AdS/CFT Correspondence
• Proper time to the black hole singularity from thermal one-point functions
• Maximum Tension: with and without a cosmological constant
• A Safe Beginning for the Universe?
• Return of the quantum cosmic censor
• Lorentz violation and black-hole thermodynamics
• Classical versus quantum completeness
• Are Black Holes Springy?
• Finite Action Principle Revisited
• Extremal black holes, gravitational entropy and nonstationary metric fields
• Black Hole Final State Conspiracies
• Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms
• Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime
• Hawking radiation may violate the Penrose cosmic censorship conjecture
• Black Hole Entropy is Thermodynamic Entropy
• Is thermodynamics fundamental?
• Saturating The Bekenstein-Hawking Entropy Bound With Initial Data Sets For Gravitational Collapse
• Future Boundaries and the Black Hole Information Paradox