Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries

TL;DR

This paper demonstrates that near-horizon field equations in both Einstein and Lanczos-Lovelock gravity can be interpreted as thermodynamic identities, extending the thermodynamic perspective of gravity beyond Einstein's theory.

Contribution

It generalizes the thermodynamic interpretation of near-horizon field equations to Lanczos-Lovelock gravity, showing this extends beyond Einstein's theory.

Findings

Near-horizon Einstein equations can be written as thermodynamic identities.

The thermodynamic interpretation applies to Lanczos-Lovelock gravity.

The highly symmetric form of Einstein tensor near horizons underpins this interpretation.

Abstract

It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon field equations again represent a thermodynamic identity in all these models. These results confirm the conjecture that this thermodynamic perspective of gravity extends far beyond Einstein's theory.