Thermodynamic Black Holes.

George Ruppeiner

doi:10.3390/e20060460

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-Nordström black holes for guidance, and find candidate equations of state that embody several 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.

Highlights

Thermodynamics rests on general principles spanning a wide range of physical systems, from pure fluids to black holes
This is the basic justification in the modern theory of critical phenomena for regarding only the dimensionalities of the physical space and of the order parameter to be relevant for determining the universal properties [38]
I have argued that fundamental properties about black hole thermodynamics might be obtained by thermodynamic means

Summary

Introduction

Thermodynamics rests on general principles spanning a wide range of physical systems, from pure fluids to black holes. I focus here on the theory of black holes that has been brought into thermodynamics via black hole thermodynamics (BHT) [1]. The idea contributed in this paper is that there is basic thermodynamic information to be found by considering the interplay between macroscopic and mesoscopic size scales in a system. This viewpoint is applied by linking the thermodynamic curvature R with the free energy φ from the theory of critical phenomena. We might reasonably expect this method to extend to the black hole scenario

Methods

Results

Discussion

Conclusion