Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

TL;DR

This paper extends the thermodynamic interpretation of geometrical variables from general relativity to Lanczos-Lovelock gravity, identifying conjugate variables that relate surface term variations to entropy and temperature on horizons.

Contribution

It introduces two geometrical variables in Lanczos-Lovelock models that generalize known conjugate variables in general relativity, linking surface term variations to thermodynamic quantities.

Findings

Variables reduce to GR case in the appropriate limit

Surface term variations correspond to $S ext{delta}T$ and $T ext{delta}S$

Identifies Wald entropy as the thermodynamic entropy in Lanczos-Lovelock models

Abstract

It has been shown in an earlier work [arXiv:1303.1535] that there exists a pair of canonically conjugate variables $(f^{ab},N^a_{bc})$ in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations $(f^{bc}\delta N^a_{bc}, N^a_{bc}\delta f^{bc})$, 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.