Stability of mass varying particle lumps

TL;DR

This paper analyzes the stability of mass-varying particle structures, like dark matter or neutrino lumps, using Einstein equations, revealing conditions for stability and the existence of black-hole-like solutions.

Contribution

It provides a stability analysis of static, spherically symmetric solutions with mass-varying particles mediated by a scalar field, exploring their potential to resemble black holes.

Findings

Solutions become unstable beyond certain mass-radius ratios.

Regular solutions can mimic Schwarzschild black holes.

Uncertainty remains about the existence of stable, regular solutions.

Abstract

The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric solutions of Einstein equations for a system composed by nonbaryonic matter (neutrinos or dark matter) which forms stable structures through attractive forces mediated by a background scalar-field (dark energy). Assuming that the dark matter, or massive neutrinos, consist of a gas of weakly interacting particles, the coupling with the scalar field is translated into an effective dependence of the mass of the compounding particle on the radial coordinate of the curved spacetime. The stability analysis reveals that these static solutions become dynamically unstable for different Buchdahl limits of the ratio between the total mass-energy and the stellar radius, $M/R$. We also find regular solutions that for an external observer resemble Schwarzschild black-holes. Our analysis leaves unanswered the question whether such solutions, which are both regular and stable, do exist.