Thermodynamics of Gravity in Local Frames

TL;DR

This paper investigates the thermodynamic properties of gravity in local inertial frames, showing that local horizons exhibit temperature under certain conditions, thus linking gravity and thermodynamics at small scales.

Contribution

It demonstrates that local Rindler horizons in curved spacetime are thermally active, extending the thermodynamic perspective of gravity to local inertial frames.

Findings

Local horizons are hot when $aL>>1$

Thermodynamic properties of gravity hold in local inertial frames

Curvature effects appear in Riemann normal coordinates

Abstract

We probe the thermodynamic structure of gravity at local scales. In any general curved spacetime, it is possible to transform to a local inertial frame at any point such that the metric is flat up to quadratic order where the curvature at that point comes in when the metric is written in Riemann normal coordinates. We consider local Rindler observers in that patch and hence the local Rindler horizon. In doing so, we find that the local horizons are also hot provided the $aL>>1$ which can always be satisfied.