Uniformly accelerating observer in $\kappa$-deformed space-time

Abstract

In this paper, we study the effect of $\kappa$-deformation of the space-time on the response function of a uniformly accelerating detector coupled to a scalar field. Starting with $\kappa$-deformed Klein-Gordon theory, which is invariant under a $\kappa$-Poincar\'e algebra and written in commutative space-time, we derive $\kappa$-deformed Wightman functions, valid up to second order in the deformation parameter $a$. Using this, we show that the first non-vanishing correction to the Unruh thermal distribution is only in the second order in $a$. We also discuss various other possible sources of $a$-dependent corrections to this thermal distribution.