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 relativistic deformed 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.

Black Hole Surface Gravity in Doubly Special Relativity Geometries / Javier Relancio, Josè; Liberati, Stefano. - In: UNIVERSE. - ISSN 2218-1997. - 8:2(2022), pp. 1-15. [10.3390/universe8020136]

Black Hole Surface Gravity in Doubly Special Relativity Geometries

Stefano Liberati
2022-01-01

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 relativistic deformed 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.
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https://doi.org/10.3390/universe8020136
https://arxiv.org/abs/2109.12336
Javier Relancio, Josè; Liberati, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128351
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