Lanczos-Lovelock gravity from a thermodynamic perspective

TL;DR

This paper extends the thermodynamic perspective of gravitational field equations to Lanczos-Lovelock gravity, demonstrating that key results linking horizon thermodynamics and gravity in general relativity also hold in this more general framework.

Contribution

It generalizes the thermodynamic interpretation of gravitational equations from general relativity to Lanczos-Lovelock gravity, including near-horizon and null surface analyses.

Findings

Field equations near horizons can be expressed as thermodynamic identities.

Results from general relativity extend straightforwardly to Lanczos-Lovelock gravity.

Thermodynamic interpretation applies to arbitrary null surfaces in Lanczos-Lovelock gravity.

Abstract

The deep connection between gravitational dynamics and horizon thermodynamics leads to several intriguing features both in general relativity and in Lanczos-Lovelock theories of gravity. Recently in arXiv:1312.3253 several additional results strengthening the above connection have been established within the framework of general relativity. In this work we provide a generalization of the above setup to Lanczos-Lovelock gravity as well. To our expectation it turns out that most of the results obtained in the context of general relativity generalize to Lanczos-Lovelock gravity in a straightforward but non-trivial manner. Another very interesting feature for gravity is that gravitational field equations for arbitrary static and spherically symmetric spacetimes with horizon can be written as a thermodynamic identity in the near horizon limit. This result holds in both general relativity and in Lanczos-Lovelock gravity as well. In a previous work [arXiv:1505.05297] we have shown that, for an arbitrary spacetime, the gravitational field equations near any null surface generically leads to a thermodynamic identity. In this work, we have also generalized this result to Lanczos-Lovelock gravity by showing that gravitational field equations for Lanczos-Lovelock gravity near an arbitrary null surface can be written as a thermodynamic identity. By taking appropriate limit to general relativity we can reproduce the results presented in arXiv:1312.3253 and arXiv:1505.05297.