Modified Unruh effect from generalized uncertainty principle

Abstract

We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dependence on the cubic power of the acceleration of the reference frame. The dependence of the shifted temperature on the frequency is also pointed out and discussed.

Unruh effect for interacting particles with ultracold atoms

“…Conversely, deviations from such behavior can signal e.g. the breaking of Lorentz invariance [151], the deformation of the uncertainty principle [152], or even open a window on quantum gravity [153].…”

Quantum phenomenological gravitational dynamics: a general view from thermodynamics of spacetime

“…where ψ is a real number that can be expected to be of the order of unity [49,50]. The existence of any such corrections to the Unruh (or even Hawking) temperature remains uncertain and, to our best knowledge, the modified temperature was not reproduced by any rigorous method.…”

“…Since δS m directly depends on the Unruh temperature, its possible modifications due to quantum gravity effects need to be considered. Recently, quantum gravity corrections to the Unruh temperature formula were suggested in the context of GUP [49,50], following earlier proposal of such corrections to Hawking temperature [5]. While several slightly different formulas appear in the literature, all include a leading order correction term proportional to T 3 ∝ a 3 , with T being the standard Unruh temperature.…”

Investigation of Unruh temperature of black holes by using the EGUP formalism

“…We follow [36,37,38], and then, the distance along which each particle must be accelerated in order to create N pairs is ∆X that we use ∆X = 2N c 2 a and ∆E = 3 2 k B T in eq. (8).…”