Thermodynamic Black Holes

TL;DR

This paper proposes a thermodynamic framework using information geometry to select black hole equations of state, potentially bridging gravitational and quantum aspects without requiring detailed microscopic theories.

Contribution

It introduces a parameterized thermodynamic approach for black holes, accommodating observational and theoretical data, and emphasizes the role of critical phenomena in black hole thermodynamics.

Findings

Candidate equations of state for Kerr and Reissner-Nordstrom black holes identified

Approach models black hole microstructure effects through thermodynamic criticality

Framework allows for integration of observational data into thermodynamic models

Abstract

Black holes pose great difficulties for theory since gravity and quantum theory must be combined in some as yet unknown way. An additional difficulty is that detailed black hole observational data to guide theorists is lacking. In this paper, I sidestep the difficulties of combining gravity and quantum theory by employing black hole thermodynamics augmented by ideas from the information geometry of thermodynamics. I propose a purely thermodynamic agenda for choosing correct candidate black hole thermodynamic scaled equations of state, parameterized by two exponents. These two adjustable exponents may be set to accommodate additional black hole information, either from astrophysical observations or from some microscopic theory, such as string theory. My approach assumes implicitly that the as yet unknown microscopic black hole constituents have strong effective interactions between them, of a type found in critical phenomena. In this picture, the details of the microscopic interaction forces are not important, and the essential macroscopic picture emerges from general assumptions about the number of independent thermodynamic variables, types of critical points, boundary conditions, and analyticity. I use the simple Kerr and Reissner-Nordstrom black holes for guidance, and find candidate equations of state that embody a number of the features of these purely gravitational models. My approach may offer a productive new way to select black hole thermodynamic equations of state representing both gravitational and quantum properties.