Self-gravitating fluid systems and galactic dark matter

• Published in: General relativity and gravitation 2017-09, Vol.49 (9), p.1-21, Article 116
• Main Authors: Banik, Uddipan, Dey, Dipanjan, Bhattacharya, Kaushik, Sarkar, Tapobrata
• Format: Article
• Language: English
• Subjects: Astronomical models; Astronomy; Astrophysics and Cosmology; Circular orbits; Classical and Quantum Gravitation; Collapse; Computational fluid dynamics; Dark matter; Defects; Differential Geometry; Fluids; Gravitation; Gravitational collapse; Gravity; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativism; Relativity Theory; Research Article; Theoretical
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-017-2284-x

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.