Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

Abstract

It has been shown in an earlier work [arXiv:1303.1535] that there exists a pair of canonically conjugate variables $(f^{ab},N_{bc}^a)$ in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations $(f^{bc}\delta N_{bc}^a,N_{bc}^a\delta f^{bc})$, which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with $(S\delta T,T\delta S)$ where $(T,S)$ are the temperature and entropy. We generalize these results to Lanczos-Lovelock models in this paper. We identify two such variables in Lanczos-Lovelock models such that (a) our results reduce to that of general relativity in the appropriate limit and (b) the variation of surface term in the action, when evaluated on a null surface, has direct thermodynamic interpretation as in the case of general relativity. The variations again correspond to $S\delta T$ and $T\delta S$ where $S$ is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.

arXiv commentv2, References Modified

References in corpus (14)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Thermodynamical Aspects of Gravity: New insights
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• The Thermodynamics of Black Holes
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Lanczos-Lovelock models of gravity
• Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Dirty black holes: Spacetime geometry and near-horizon symmetries
• Noether Current, Horizon Virasoro Algebra and Entropy
• The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm

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