Hawking radiation in the kappa-spacetime

TL;DR

This paper investigates how non-commutative kappa-deformation affects Hawking radiation and temperature of Schwarzschild black holes, revealing modifications due to the underlying spacetime structure.

Contribution

It derives a deformed Schwarzschild metric in kappa-spacetime and calculates the resulting changes in Hawking radiation and temperature.

Findings

Hawking temperature is modified by kappa-deformation.

Deformed metric depends on energy and momentum.

Hawking radiation spectrum is altered in kappa-spacetime.

Abstract

In this paper, we analyze the Hawking radiation of a kappa-deformed Schwarzchild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the kappa-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzchild metric obtained in the kappa-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1+1 dimensions, to solve the kappa-deformed Klein-Gordon equation in the background of the Schwarzchild metric. The method of Boguliobov coefficients is then used to calculate the thermal spectrum of kappa-deformed-Schwarzchild black hole and show that the Hawking temperature is modified by the non-commutativity of the kappa-spacetime.