Galactic space-times in modified theories of gravity

Abstract

We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.

1 + 29 Pages, LaTeX, 12 .eps figures. Some discussions improved. Published version

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• A method for evaluating models that use galaxy rotation curves to derive the density profiles
• Self-gravitating fluid systems and galactic dark matter
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• Post-Newtonian properties of EMRI with Power Law Potential
• Rotation curves and orbits in the scalar field dark matter halo spacetime