Accelerated Observers, Thermal Entropy, and Spacetime Curvature

TL;DR

This paper explores the thermodynamic properties of horizons in curved spacetime, linking entropy changes to Einstein tensor components and proposing a universal curvature correction to thermal entropy at high temperatures.

Contribution

It establishes a connection between horizon area changes, Einstein tensor components, and thermodynamics for accelerated observers in curved spacetime, and introduces a conjecture on universal curvature corrections at high temperatures.

Findings

Horizon area change encodes information about the Einstein tensor.

The Einstein tensor can be inferred from thermodynamic considerations of accelerated observers.

A conjecture on universal curvature correction to entropy at high temperatures.

Abstract

Assuming that an accelerated observer with four-velocity ${\bf u}_{\rm R}$ in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", we show that the $\rm \it change$ in horizon area under parametric displacements of the horizon has a very specific thermodynamic structure. Specifically, it entails information about the time-time component of the Einstein tensor: $\bf G({\bf u}_{\rm R}, {\bf u}_{\rm R})$. Demanding that the result holds for all accelerated observers, this actually becomes a statement about the full Einstein tensor, $\rm \bf G$. We also present some perspectives on the free fall with four-velocity ${\bf u}_{\rm ff}$ across the horizon that leads to such a loss of entropy for an accelerated observer. Motivated by results for some simple quantum systems at finite temperature $T$, we conjecture that at high temperatures, there exists a universal, system-independent curvature correction to partition function and thermal entropy of $\rm \it any$ freely falling system, characterised by the dimensional quantity $\Delta = {\bf R({\bf u}_{\rm ff}, {\bf u}_{\rm ff})} \left(\hbar c/kT \right)^2$.