$κ-$Minkowski spacetime and a uniformly accelerating observer

Kim, Hyeong-Chan; Yee, Jae Hyung; Rim, Chaiho

$κ-$Minkowski spacetime and a uniformly accelerating observer

Authors

Kim, Hyeong-Chan

Yee, Jae Hyung

Rim, Chaiho

Description

We analyze the response of a detector with a uniform acceleration $α$ in $κ-$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 $κ-$deformation. The response function deviates from the thermal distribution of Unruh temperature at the order of $1/κ$ and vanishes exponentially as the proper time of the detector exceeds a certain critical time, a logarithmic function of $κ$. This suggests that the Unruh temperature becomes not only fuzzy but also eventually decreases to zero in this model.
13 pages, 2 figures