Unruh temperatures in circular and drifted Rindler motions

TL;DR

This paper investigates how Unruh temperatures vary for circular and drifted Rindler motions using the Unruh-DeWitt detector, revealing nonlinear behaviors and conditions under which temperature vanishes or peaks.

Contribution

It provides a detailed analysis of Unruh temperatures in circular and drifted Rindler motions, highlighting nonlinear dependencies and new temperature behaviors near infinite proper acceleration.

Findings

Temperature peaks at a certain radius in circular motion

Temperature behaves like the usual Unruh effect at slow transverse velocities

Temperature vanishes at the speed of light in the transverse direction

Abstract

We study the temperatures for the circular and drifted Rindler motions by employing the Unruh-DeWitt detector method. In the circular motion, the temperature is increasing along the radius of the circular motion until it reaches the maximum, and then it is decreasing and eventually vanishing at the limit to the radius where the proper acceleration is infinite. In fact, the temperature is proportional to the proper acceleration quadratically near the origin of the circular motion as compared to the usual Unruh effect depending on the linear proper acceleration. On the other hand, in the drifted Rindler motion, the observer moves with a relative velocity in the direction transverse to the acceleration. If the detector is moving slowly in the transverse direction with a finite proper acceleration, then the temperature behaves like the usual Unruh temperature, while it vanishes for the speed of light in the transverse direction according to the infinite proper acceleration. Consequently, it turns out that the temperatures behave nonlinearly with respect to the proper acceleration and the infinite proper acceleration would not always permit the divergent temperature.