$\kappa-$Minkowski spacetime and a uniformly accelerating observer

TL;DR

This paper investigates how a uniformly accelerating detector in $$-Minkowski spacetime perceives the vacuum, revealing deviations from the Unruh effect due to spacetime noncommutativity, leading to a diminishing perceived temperature over time.

Contribution

It introduces a model of a detector in $$-Minkowski spacetime that incorporates Lorentz violation effects from noncommutative geometry, analyzing its response function.

Findings

Response deviates from thermal Unruh distribution at order 1/κ.

Response function vanishes exponentially after a critical proper time.

Unruh temperature effectively decreases to zero over time.

Abstract

We analyze the response of a detector with a uniform acceleration $\alpha$ in $\kappa-$Minkowski spacetime using the first order perturbation theory. The monopole detector is coupled to a massless complex scalar field in such a way that it is sensitive to the Lorentz violation due to the noncommutativity of spacetime present in the $\kappa-$deformation. The response function deviates from the thermal distribution of Unruh temperature at the order of $1/\kappa$ and vanishes exponentially as the proper time of the detector exceeds a certain critical time, a logarithmic function of $\kappa$. This suggests that the Unruh temperature becomes not only fuzzy but also eventually decreases to zero in this model.