Black hole surface gravity in doubly special relativity geometries

TL;DR

This paper investigates the concept of surface gravity in a quantum gravity-inspired, momentum-dependent black hole geometry, revealing that different definitions of surface gravity generally differ except in a specific momentum basis.

Contribution

It introduces a study of surface gravity in a momentum-dependent Schwarzschild black hole, highlighting the basis-dependent agreement of various definitions.

Findings

Two main notions of surface gravity yield momentum-independent results.

Different definitions agree only in a specific momentum basis.

Supports the physical relevance of a particular momentum basis.

Abstract

In a quantum gravity theory, spacetime at mesoscopic scales can acquire a novel structure very different from the classical concept of general relativity. A way to effectively characterize the quantum nature of spacetime is through a momentum dependent space-time metric. There is a vast literature showing that this geometry is related to deformed relativistic kinematics, which is precisely a way to capture residual effects of a quantum gravity theory. In this work, we study the notion of surface gravity in a momentum dependent Schwarzschild black hole geometry. We show that using the two main notions of surface gravity in general relativity we obtain a momentum independent result. However, there are several definitions of surface gravity, all of them equivalent in general relativity when there is a Killing horizon. We show that in our scheme, despite the persistence of a Killing horizon, these alternative notions only agree in a very particular momentum basis, obtained in a previous work, so further supporting its physical relevance.