Galactic Dark Matter and Bertrand Space-times

Abstract

Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies move in such orbits, we propose that, under certain physical assumptions, the dark matter distribution of some low surface brightness (LSB) galaxies can seed a particular class of BSTs. In the Newtonian limit, it is shown that for flat rotation curves, our proposal leads to an analytic prediction of the NFW dark matter profile. We further show that the dark matter distribution that seeds the BST, is described by a two-fluid anisotropic model, and present its analytic solution. A new solution of the Einstein's equations, with an internal BST and an external Schwarzschild metric, is also constructed.

1+21 Pages, LaTeX, 9 .eps figures. Minor changes. Version published in PRD

References in corpus (7)

• The Universal Rotation Curve of Spiral Galaxies. II The Dark Matter Distribution out to the Virial Radius
• On the local dark matter density
• Can strong gravitational lensing distinguish naked singularities from black holes?
• Two-fluid dark matter models
• Bertrand spacetimes as Kepler/oscillator potentials
• Possible potentials responsible for stable circular relativistic orbits
• Geodesic Congruences and Their Deformations in Bertrand Space-times

Cited by in corpus (19)

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• Shadows and precession of orbits in rotating Janis-Newman-Winicour spacetime
• Precession of timelike bound orbits in Kerr spacetime
• Towards an observational test of black hole versus naked singularity at the galactic center
• Perihelion Precession and Shadows near Blackholes and Naked Singularities
• Astrophysics of Bertrand Space-times
• Globally visible singularity in an astrophysical setup
• Light trajectory and shadow shape in the rotating naked singularity
• Tidal Forces in Naked Singularity Backgrounds
• Comparing thin accretion disk properties of naked singularities and black holes
• Self-gravitating fluid systems and galactic dark matter
• Galactic space-times in modified theories of gravity
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• Fermi Normal Coordinates and Fermion Curvature Couplings in General Relativity
• Dark matter candidate induced by Horndeski theory: dark matter halo and cosmological evolution
• Post-Newtonian properties of EMRI with Power Law Potential