Tolman temperature once again: A derivation from gravitational surface action

TL;DR

This paper derives the Tolman temperature distribution using the Gibbons-Hawking-York surface term without relying on Einstein's equations, providing an off-shell perspective on gravitational thermodynamics.

Contribution

It presents a novel off-shell derivation of the Tolman temperature from gravitational surface action, avoiding the use of Einstein's equations.

Findings

Derivation of Tolman temperature from surface term alone

Off-shell analysis of gravitational thermodynamics

Discussion of implications for gravitational physics

Abstract

The temperature distribution in presence of gravity, as measured by a local observer, is given by the Tolman expression. Here I derive the same only from the Gibbon's-Hawking-York surface term. In this process no explicit use of Einstein's equations of motion is done. Therefore, the present one is an off-shell analysis. Finally I discuss the importance and various implications of the derivation.