English

Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

General Relativity and Quantum Cosmology 2014-12-05 v2

Abstract

It has been shown in an earlier work [arXiv:1303.1535] that there exists a pair of canonically conjugate variables (fab,Nbca)(f^{ab},N^a_{bc}) in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations (fbcδNbca,Nbcaδfbc)(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 (SδT,TδS)(S\delta T,T\delta S) where (T,S)(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 SδTS\delta T and TδST\delta S where SS is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.

Keywords

Cite

@article{arxiv.1408.4791,
  title  = {Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity},
  author = {Sumanta Chakraborty and T. Padmanabhan},
  journal= {arXiv preprint arXiv:1408.4791},
  year   = {2014}
}

Comments

v2, References Modified