Self-gravitating fluid systems and galactic dark matter

TL;DR

This paper explores gravitational collapse with anisotropic pressures leading to space-times that could model galactic dark matter, revealing stable orbits, naked singularities, and potential exotic matter components.

Contribution

It identifies a class of space-times with conical defects from collapse, showing they can mimic dark matter halos with stable orbits and exotic matter features.

Findings

Space-times with conical defects can produce stable circular orbits at all radii.

Galactic space-times may involve exotic matter with negative pressure.

Newtonian two-fluid models align with relativistic predictions for dark matter scenarios.

Abstract

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two- fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.