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

TL;DR

This paper investigates how $mbda$-deformation of space-time influences the response of a uniformly accelerating detector, revealing that leading corrections to the Unruh effect appear only at second order in the deformation parameter.

Contribution

It derives $mbda$-deformed Wightman functions and shows that first-order corrections to the Unruh thermal distribution vanish, highlighting the second-order effects of space-time deformation.

Findings

First non-zero correction appears at second order in deformation parameter

Derived $mbda$-deformed Wightman functions up to second order

Discussed potential sources of $a$-dependent corrections to Unruh temperature

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.