Abstract
Employing the covariant phase space formalism, we discuss black hole thermodynamics in four-dimensional scalar-tensor Einstein-Gauss-Bonnet gravity. We argue that logarithmic corrections to Wald entropy previously reported in this theory do not appear, due to the symmetry of the theory under constant shifts of the scalar field. Instead, we obtain the standard Bekenstein entropy of general relativity. Then, to satisfy the first law of black hole mechanics, the Hawking temperature must be modified. It has been proposed that such temperature modifications occur generically in scalar-tensor theories, due to different propagation speeds of gravitons and photons. We show that the temperature modifications also emerge in the Euclidean canonical ensemble approach to black hole thermodynamics. Notably, the boundary terms of the type we consider here can be considered in any scalar-tensor gravitational theories. Hence, we illustrate that adding a suitable boundary term to action may drastically affect black hole thermodynamics, changing both the entropy and the temperature.
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Acknowledgments
We would like to thank Pablo Cano for useful comments on our work. M.L. is supported by the Charles University Grant Agency project No. GAUK 90123. RAH is grateful to Andrew Svesko for a number of helpful discussions at the Benasque 2023 workshop, “Gravity: New Perspectives from Strings and Higher Dimensions”. The work of RAH received the support of a fellowship from “la Caixa” Foundation (ID 100010434) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 847648 under fellowship code LCF/BQ/PI21/11830027. D.K. is grateful for support from GAČR 23-07457S grant of the Czech Science Foundation.
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Liška, M., Hennigar, R.A. & Kubizňák, D. No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity. J. High Energ. Phys. 2023, 195 (2023). https://doi.org/10.1007/JHEP11(2023)195
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DOI: https://doi.org/10.1007/JHEP11(2023)195