Thermodynamic route to Field equations in Lanczos-Lovelock Gravity

TL;DR

This paper extends the thermodynamic interpretation of gravitational field equations to Lanczos-Lovelock gravity, showing that these equations can also be derived from horizon thermodynamics, indicating a deep connection between thermodynamics and quantum corrections in gravity.

Contribution

It demonstrates that the thermodynamic relation TdS = dE + PdV applies to Lanczos-Lovelock gravity, generalizing previous results beyond Einstein-Hilbert gravity.

Findings

Field equations for Lanczos-Lovelock gravity can be expressed as thermodynamic identities.

The thermodynamic relation holds for higher-order gravity theories.

Quantum corrections relate to the structure of the theory via the expansion of Q^{abcd}.

Abstract

Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS = dE + PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS = dE + PdV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L=Q_a^{bcd}R^a_{bcd} with \nabla_b Q^{abcd}=0. In such models, the expansion of Q^{abcd} in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation TdS = dE + PdV has a greater domain of validity that Einstein's field equations.