Thermodynamic Properties of Spherically-Symmetric, Uniformly-Accelerated Reference Frames

TL;DR

This paper investigates the thermodynamic properties of spherically symmetric uniformly accelerated reference frames, revealing that horizon thermodynamics laws do not generally apply, and emphasizing the distinction between temperature as a kinematic effect and thermodynamic laws.

Contribution

It introduces a generalization of Rindler frames and shows that horizon thermodynamics do not hold universally in these frames, highlighting the role of dynamics in thermodynamic laws.

Findings

Horizon thermodynamics laws do not apply in general for these frames.

Hawking-Unruh temperature is a kinematic effect, not sufficient for thermodynamics.

Common horizons may not exist for all uniformly accelerated observers.

Abstract

We aim to study the thermodynamic properties of the spherically symmetric reference frames with uniform acceleration, including the spherically symmetric generalization of Rindler reference frame and the new kind of uniformly accelerated reference frame. We find that, unlike the general studies about the horizon thermodynamics, one cannot obtain the laws of thermodynamics for their horizons in the usual approaches, despite that one can formally define an area entropy (Bekenstein-Hawking entropy). In fact, the common horizon for a set of uniformly accelerated observers is not always exist, even though the Hawking-Unruh temperature is still well-defined. This result indicates that the Hawking-Unruh temperature is only a kinematic effect, to gain the laws of thermodynamics for the horizon, one needs the help of dynamics. Our result is in accordance with those from the various studies about the acoustic black holes.