Exploring black hole mechanics in cotangent bundle geometries

TL;DR

This paper investigates black hole thermodynamics within a modified geometric framework where the metric depends on both position and momentum, inspired by doubly special relativity, revealing potential new insights into quantum gravity effects.

Contribution

It introduces a cotangent bundle metric approach to black hole thermodynamics compatible with deformed relativistic kinematics, extending previous momentum space geometries to curved spacetimes.

Findings

First two laws of black hole thermodynamics are formulated in this new framework.

The momentum-dependent metric influences black hole properties and thermodynamic behavior.

Potential implications for quantum gravity phenomenology are discussed.

Abstract

The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to characterize this modified space-time notion is by a momentum dependent metric, in such a way that particles with different energies could probe different spacetimes. Indeed, doubly special relativity theories, deforming the special relativistic kinematics while maintaining a relativity principle, have been understood within a geometrical context, by considering a curved momentum space. The extension of these momentum spaces to curved spacetimes and its possible phenomenological implications have been recently investigated. Following this line of research, we address here the first two laws of black holes thermodynamics in the context of a cotangent bundle metric, depending on both momentum and space-time coordinates, compatible with the relativistic deformed kinematics of doubly special relativity.