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Entropy 2018, 20(6), 460;

Thermodynamic Black Holes

Division of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, FL 34243, USA
Received: 10 April 2018 / Revised: 6 June 2018 / Accepted: 11 June 2018 / Published: 13 June 2018
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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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. View Full-Text
Keywords: black hole thermodynamics; information geometry of thermodynamics; thermodynamic curvature; Kerr black hole; Reissner-Nordström black hole; critical phenomena black hole thermodynamics; information geometry of thermodynamics; thermodynamic curvature; Kerr black hole; Reissner-Nordström black hole; critical phenomena

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Ruppeiner, G. Thermodynamic Black Holes. Entropy 2018, 20, 460.

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