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Horizon thermodynamics and gravitational field equations in quasi-topological gravity

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Abstract

In this paper we show that the gravitational field equations of \((n+1)\)-dimensional topological black holes with constant horizon curvature, in cubic and quartic quasi-topological gravity, can be recast in the form of the first law of thermodynamics, \(dE=TdS-PdV\), at the black hole horizon. This procedure leads to extract an expression for the horizon entropy as well as the energy (mass) in terms of the horizon radius, which coincide exactly with those obtained in quasi-topological gravity by solving the field equations and using the Wald’s method. We also argue that this approach is powerful enough to be extended to all higher order quasi-topological gravity for extracting the corresponding entropy and energy in terms of horizon radius.

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Acknowledgments

We thank from the Research Council of Shiraz University. This work has been supported financially by Research Institute for Astronomy & Astrophysics of Maragha (RIAAM), Iran.

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Authors and Affiliations

  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, 71454 , Shiraz, Iran

    A. Sheykhi, M. H. Dehghani & R. Dehghani

  2. Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

    A. Sheykhi & M. H. Dehghani

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  1. A. Sheykhi
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  2. M. H. Dehghani
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  3. R. Dehghani
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Correspondence to A. Sheykhi.

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Sheykhi, A., Dehghani, M.H. & Dehghani, R. Horizon thermodynamics and gravitational field equations in quasi-topological gravity. Gen Relativ Gravit 46, 1679 (2014). https://doi.org/10.1007/s10714-014-1679-1

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