The Effect of Modified Dispersion Relation on Dumb Holes

TL;DR

This paper investigates how deforming the photon gas dispersion relation affects dumb hole physics, altering thermodynamics, sound velocity, horizon position, and Hawking radiation, suggesting dumb holes as potential probes for quantum gravity effects.

Contribution

It introduces a novel analysis of how modified dispersion relations influence dumb hole thermodynamics and horizon properties, proposing their use in testing quantum gravity theories.

Findings

Modified dispersion relation changes thermodynamic properties.

Sound velocity in dumb holes is affected.

Horizon position and Hawking radiation are altered.

Abstract

In this paper, we will deform the usual energy-momentum dispersion relation of a photon gas at an intermediate scale between the Planck and electroweak scales. We will demonstrate that such a deformation can have non-trivial effects on the physics of dumb holes. So, motivated by the physics of dumb holes, we will first analyse the effect of such a deformation on thermodynamics. Then we observe that the velocity of sound also gets modified due to such a modification of the thermodynamics. This changes the position of the horizon of a dumb hole, and the analogous Hawking radiation from a dumb hole. Therefore, dumb holes can be used to measure the deformation of the usual energy-momentum dispersion relation.