$\kappa$--Rindler space

TL;DR

This paper constructs a non-commutative version of Rindler space called $appa$--Rindler space, analyzes its thermal properties, and derives leading order quantum corrections to Hawking radiation.

Contribution

It introduces the $appa$--Rindler space as a non-commutative counterpart of Rindler space and computes quantum corrections to Hawking radiation using star product techniques.

Findings

Derived the commutator structure of $appa$--Rindler space.

Calculated the leading order $1/ppa$ correction to Hawking spectrum.

Established a framework for studying thermal properties in non-commutative spacetime.

Abstract

In this paper we construct, and investigate some thermal properties of, the non-commutative counterpart of Rindler space, which we call $\kappa$--Rindler space. This space is obtained by changing variables in the defining commutators of $\kappa$--Minkowski space. We then re-derive the commutator structure of $\kappa$--Rindler space with the help of an appropriate star product, obtained from the $\kappa$--Minkowski one. Using this star product, following the idea of Padmanabhan, we find the leading order, $1/\kappa$ correction to the Hawking thermal spectrum.