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Free Energy of Topologically Massive Gravity and Flat Space Holography

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2nd Karl Schwarzschild Meeting on Gravitational Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 208))

Abstract

We calculate the free energy from the on-shell action for topologically massive gravity with negative and vanishing cosmological constant, thereby providing a first principles derivation of the free energy of Bañados–Teitelboim–Zanelli black holes and flat space cosmologies. We summarize related recent checks of flat space holography.

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Notes

  1. 1.

    We stress that for finite \(\mu \) entropy (10.13) does not obey the Bekenstein–Hawking area law. Nevertheless, it is compatible with the Cardy formula in the presence of a gravitational anomaly, i.e., the left- and right-moving central charges are not equal, \(c-\bar{c} = 3/(\mu G)\) [20].

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Acknowledgements

We thank Arjun Bagchi for collaboration on n-point correlation functions in flat space holography. DG additionally thanks Arjun Bagchi, Stephane Detournay, Max Riegler, Jan Rosseel and Joan Simon for a wonderful long-term collaboration on numerous aspects of flat space holography.

DG was supported by projects of the Austrian Science Fund (FWF) Y 435-N16, I 952-N16 and I 1030-N27, and by the program Science without Borders, project CNPq-401180/2014-0. WM was supported by the FWF project P 27182-N27.

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Authors and Affiliations

  1. Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    D. Grumiller & W. Merbis

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  1. D. Grumiller
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Correspondence to D. Grumiller .

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Editors and Affiliations

  1. Frankfurt Institute for Advanced Studies, Goethe University Frankfurt, Frankfurt, Hessen, Germany

    Piero Nicolini

  2. Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL, USA

    Matthias Kaminski

  3. Seaver Science Center, Loyola Marymount University, Los Angeles, CA, USA

    Jonas Mureika

  4. Institut für Theoretische Physik, Goethe-Universität, Frankfurt, Hessen, Germany

    Marcus Bleicher

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Grumiller, D., Merbis, W. (2018). Free Energy of Topologically Massive Gravity and Flat Space Holography. In: Nicolini, P., Kaminski, M., Mureika, J., Bleicher, M. (eds) 2nd Karl Schwarzschild Meeting on Gravitational Physics. Springer Proceedings in Physics, vol 208. Springer, Cham. https://doi.org/10.1007/978-3-319-94256-8_10

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