Quasi-homologous spherically symmetric branes and their symmetry breaking

TL;DR

This paper investigates the dynamics of spherically symmetric vacuum braneworlds, revealing a transcritical bifurcation related to dark pressure and analyzing the impact of the brane cosmological constant on symmetry properties.

Contribution

It introduces a dynamical system approach to braneworlds, highlighting a bifurcation phenomenon and examining the role of the cosmological constant in symmetry considerations.

Findings

Identification of a transcritical bifurcation as dark pressure changes sign

Analysis of the effects of the brane cosmological constant on symmetry

Demonstration that isothermal states cannot arise from quasi-homologous symmetry

Abstract

We revisit the dynamical system based approach of spherically symmetric vacuum braneworlds, pointing out and studying the existence of a transcritical bifurcation as the dark pressure parameter changes its sign, we analyze some consequences of not discard the brane cosmological constant. For instance, it is noteworthy that the existence of an isothermal state equation between the dark fluid parameters cannot be obtained via the requirement of a quasi-homologous symmetry of the vacuum.