Stability of the graviton Bose–Einstein condensate in the brane-world

Roldão Da Rocha,Roberto Casadio

doi:10.1016/j.physletb.2016.10.072

Abstract

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic E\"otv\"os brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose-Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.

Highlights

Several aspects of black hole physics have been recently studied, by considering black holes as Bose–Einstein condensates (BEC) of a large number N of weakly interacting, long-wavelength, gravitons close to a critical point [1,2,3]
Studying a Minimal Geometric Deformation (MGD) BEC in a Eötvös brane-world scenario provides a strict bound for the brane tension σ 3.18 × 106 MeV4, which is stronger than the bound determined by the study of cosmological nucleosynthesis
Analysing the graviton BEC MGD black hole shows that it is important to take into account quantum effects at the stability critical point, even for a macroscopic number of particles

Summary

Introduction

Several aspects of black hole physics have been recently studied, by considering black holes as Bose–Einstein condensates (BEC) of a large number N of weakly interacting, long-wavelength, gravitons close to a critical point [1,2,3]. The energy density is the main ingredient to compute the information entropy In this framework, the critical stable density of a BEC MGD black hole will be here studied, by relating the stellar distribution conditional entropy and its central critical density.

Minimal geometric deformation

BEC and MGD: a brane tension bound

Variable tension model

Stability analysis of the MGD BEC

Concluding remarks