Galactic rotation curves in gravity with a nondynamical scalar
Abstract: We introduce a four-dimensional gravity action and explore the idea that the Einsteinian and galactic laws of gravitation should emerge as two different dynamical phases of the resulting theory. A new set of spacetime solutions exhibiting asymptotically flat galactic rotation curves are found. These geometries correspond to anisotropic effective pressure. We also provide an explanation of the empirical correlation between the luminosity and the slope of the velocity curve. We find an enhancement in the deflection angle of a light ray penetrating the halo, which could provide a realistic testing ground for the model as a purely geometric alternative to `dark matter'. For very large halo radii, the leading nonbaryonic contribution to the bending angle is $3\pi v2/2c2$ (v being the asymptotic rotational velocity), a constant that is lesser than the deflection predicted for an isothermal CDM halo.
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