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Thermodynamic Curvature and Black Holes

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Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 153))

Abstract

In my talk, I will discuss black hole thermodynamics, particularly what happens when you add thermodynamic curvature to the mix. Although black hole thermodynamics is a little off the main theme of this workshop, I hope nevertheless that my message will be of some interest to researchers in supersymmetry and supergravity.

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Notes

  1. 1.

    The calculation of \(R\) for the ideal Bose gas was done with a continuous density of states, and so a possible divergence of \(R\) at a Bose-Einstein phase transition with \(T>0\) would not have been revealed.

  2. 2.

    If a paper starts with a spacetime metric, and calculates the thermodynamic from the area of the event horizon, it is a general relativistic solution. If the paper starts with a Lagrangian, and a quantum action then it is beyond the scope of my talk.

  3. 3.

    The line element (10.2) transforms as a scalar, since probability is a scalar quantity. Hence, the metric elements \(g_{\alpha \beta }\) transform as the elements of a second-rank tensor, which the relation between (10.20) and (10.21) satisfies. The resulting thermodynamic curvature \(R\) transforms as a scalar. These transformation properties hold under all coordinate transformations, including those resulting from Legendre transformations. This is the case in both ordinary and black hole thermodynamics, despite erroneous claims to the contrary [64].

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Acknowledgments

I thank George Skestos for travel support, and I thank the conference organizer Stefano Bellucci of INFN for giving me the opportunity to present my work.

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Authors and Affiliations

  1. Division of Natural Sciences, New College of Florida, Sarasota, FL, 34243-2109, USA

    George Ruppeiner

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  1. George Ruppeiner
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Correspondence to George Ruppeiner .

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Editors and Affiliations

  1. Laboratori Nazionali di Frascati, National Institute of Nuclear Physics, Frascati RM, Italy

    Stefano Bellucci

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Ruppeiner, G. (2014). Thermodynamic Curvature and Black Holes. In: Bellucci, S. (eds) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity. Springer Proceedings in Physics, vol 153. Springer, Cham. https://doi.org/10.1007/978-3-319-03774-5_10

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