Dynamic stabilization of non-spherical bodies against unlimited collapse

TL;DR

This paper demonstrates that non-spherical self-gravitating bodies can resist unlimited collapse through nonlinear oscillations, with collapse only occurring after oscillation damping, providing insights into stability mechanisms beyond spherical symmetry.

Contribution

It introduces a simplified model analyzing nonlinear oscillations in spheroidal bodies, revealing how deviations from spherical symmetry stabilize against collapse.

Findings

Non-spherical bodies resist collapse due to nonlinear oscillations.

Collapse occurs only after damping of oscillations.

Regions of regular and chaotic oscillations are identified.

Abstract

We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and deviations from the spherical symmetry stop the contraction by the stabilising action of nonlinear nonspherical oscillations. A real collapse happens after damping of the oscillations due to energy losses, shock wave formation or viscosity. Detailed analysis of the nonlinear oscillations is performed using a Poincar\'{e} map construction. Regions of regular and chaotic oscillations are localized on this map.