New Spacetime Solutions for Spiral Galaxies

We find a set of spacetime solutions whose rotation curves approach a flat profile at large radii, as observed for spiral galaxies. The associated stress-energy tensor reflects a positive mass and anisotropic pressure. The spatially averaged equation of state, which parametrizes these infinity of solutions, exhibits a lower bound: $w> -\frac{1}{3}$. As examples, we present the spacetime metrics for non-ideal `dust' and `radiation'. The Einstein clusters emerge as another special class, whose EOS parameter is predicted to be given by the limiting rotational velocity as: $w=\frac{v^2}{3c^2}$. Analyzing the gravitational deflection of a light ray penetrating a large halo, we find the correction to the Einsteinian bending angle to be $\Big(\frac{2+3w}{1+3w}\Big)\pi \frac{v^2}{c^2}$.