On the Unruh effect for hyperbolic observers in spacetimes of maximal proper acceleration

TL;DR

This paper explores the concept of maximal proper acceleration in spacetime, generalizes the Unruh effect for hyperbolic observers within this framework, and predicts a maximum Unruh temperature relevant to high-energy electron acceleration experiments.

Contribution

It introduces a spacetime model with maximal proper acceleration and extends the Unruh temperature formula, revealing a maximum temperature limit for accelerated observers.

Findings

Maximal proper acceleration spacetime is physically motivated and geometrically consistent.

Unruh temperature has an upper bound in such spacetimes.

Maximum Unruh temperature is estimated for high-energy electron laser systems.

Abstract

In this work, the notion of spacetime of maximal proper acceleration is motivated as a weak form to implement general covariance and a generalized form of Einstein's equivalence principle from a physical point of view and the fundamental geometric and kinematic properties of such spaces are discussed. Thereafter the Unruh temperature formula is generalized to the case of hyperbolic observers in spacetimes of maximal proper acceleration. Such a generalization implies the existence of a maximal value for the Unruh temperature. We discuss this result for an electrodynamic model of point charged particles in a spacetime of maximal proper acceleration. It is shown that according to the model, the maximal Unruh temperature must be of order $4.8\cdot 10^{10}/N$ K for current high acceleration electron laser-plasma acceleration systems, where $N$ is the population of the typical bunch.