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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>4.8</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo> </mml:mo> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:mrow> </mml:math> for current high acceleration electron laser-plasma acceleration systems, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> is the population of the typical bunch.