147 research outputs found

    Thermodynamic Black Holes

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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-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.Comment: 37 pages, 21 figure

    Thermodynamic curvature and black holes

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    I give a relatively broad survey of thermodynamic curvature RR, one spanning results in fluids and solids, spin systems, and black hole thermodynamics. RR results from the thermodynamic information metric giving thermodynamic fluctuations. RR has a unique status in thermodynamics as being a geometric invariant, the same for any given thermodynamic state. In fluid and solid systems, the sign of RR indicates the character of microscopic interactions, repulsive or attractive. R|R| gives the average size of organized mesoscopic fluctuating structures. The broad generality of thermodynamic principles might lead one to believe the same for black hole thermodynamics. This paper explores this issue with a systematic tabulation of results in a number of cases.Comment: 27 pages, 10 figures, 7 tables, 78 references. Talk presented at the conference Breaking of Supersymmetry and Ultraviolet Divergences in extended Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small problem