Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

2014/08/31 by Sumanta Chakraborty, T. Padmanabhan, Τ. Padmanabhan · 42 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #General relativity #Lanczos resampling #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Null (SQL) #Physics #Quantum mechanics #Thermodynamics #gr-qc

paper · pdf · doi:10.1103/physrevd.90.084021

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(8) (American Physical Society) · v2, References Modified

openalex publication_date 2014/10/14 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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\ensuremathδN_bc^a,N_bc^a\ensuremathδf^bc), which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with (S\ensuremathδT,T\ensuremathδS) 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 the 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\ensuremathδT and T\ensuremathδS where S is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.

Citations

• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• The Thermodynamics of Black Holes
• Particle creation by black holes
• Generalized second law of thermodynamics in black-hole physics
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Holes and Entropy
• The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm

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