Stability of mass varying particle lumps

The theoretical description of compact structures that share some features with mass varying particles allows for a simple analysis of the 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, consists 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.