Unruh temperatures in circular and drifted Rindler motions

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.

The Horizons in Circular Accelerated Motions and Its Consequences

“…However, this value of ρ = 0 is not allowed because it defines one of the horizons of the uniform circular movement. Moreover, in the case ρ max = c/Ω, that correspond to a proper acceleration a c tending to infinite for v → c, the temperature is finite and close to zero, see [28]. Therefore, when the proper acceleration goes to infinity, the Unruh temperature remains finite as long as the velocity approaches the speed of light.…”

“…Note that for large values of the radius in the circular motion, the motion looks like the case of a uniform linear acceleration, but with a speed perpendicular to the acceleration direction. This case is investigated in [28][29][30] and the temperature for the drifted Rindler motion is obtained and compared with the temperature for the linear acceleration case.…”