Branes in Gravity's Rainbow

TL;DR

This paper explores black p-brane thermodynamics within Gravity's Rainbow framework, revealing constraints on minimum mass and the potential existence of black brane remnants influenced by different rainbow functions.

Contribution

It introduces a novel analysis of black p-branes in Gravity's Rainbow, showing how specific rainbow functions affect thermodynamics and the possibility of remnants.

Findings

Gravity's Rainbow constrains minimum black p-brane mass.

Black p-brane remnants are suggested by heat capacity analysis.

Different rainbow functions yield varying thermodynamic behaviors.

Abstract

In this work, we investigate the thermodynamics of black $p$-branes (BB) in the context of Gravity's Rainbow. We investigate this using rainbow functions that have been motivated from loop quantum gravity and $\kappa$-Minkowski noncommutative spacetime. Then for the sake of comparison, we examine a couple of other rainbow functions that have also appeared in the literature. We show that, for consistency, Gravity's Rainbow imposes a constraint on the minimum mass of the BB, a constraint that we interpret here as implying the existence of a black $p$-brane remnant. This interpretation is supported by the computation of the black $p$-brane's heat capacity that shows that the latter vanishes when the Schwarzschild radius takes on a value that is bigger than its extremal limit. We found that the same conclusion is reached for the third version of rainbow functions treated here but not with the second one for which only standard black $p$-brane thermodynamics is recovered.