Gravitational collapse in brane-worlds revisited

TL;DR

This paper investigates how brane-world modifications influence stellar gravitational collapse, analyzing the dynamics, stability, and non-local effects in a homogeneous, isotropic, closed universe model.

Contribution

It provides a detailed dynamical systems analysis of brane-world effects on stellar collapse, highlighting the role of non-local and quadratic energy-momentum corrections.

Findings

Identification of attractors and saddle points in the collapse dynamics.

Influence of brane parameters on stability and evolution.

Characterization of non-local effects during collapse.

Abstract

This paper is dedicated to revisit the modifications caused by branes in the collapse of a stellar structure under the Snyder-Oppenheimer scheme. Due to the homogeneity and isotropy of the model, we choose study the case of a closed geometry described by $k=1$, through the tool of dynamical systems. We revisit the different components of the star and its evolution during the stellar collapse, paying particular attention to the non-local effects and the quadratic terms of the energy momentum tensor that come from branes corrections. In the same vein we realize a phase portrait together with a stability analysis with the aim of obtain information about the attractors or saddle points of the dynamical system under different initial conditions in the density parameters, remarking the parameters that come from branes contributions.