New Spacetime Solutions for Spiral Galaxies

TL;DR

This paper introduces new spacetime solutions that model spiral galaxy rotation curves, showing how these solutions can explain observed flat rotation profiles and gravitational lensing effects.

Contribution

The paper presents novel spacetime metrics with specific stress-energy properties that reproduce galaxy rotation curves and predict gravitational lensing corrections.

Findings

Rotation curves approach flat profiles at large radii.

Derived spacetime metrics for non-ideal dust and radiation.

Predicted gravitational deflection correction depending on EOS parameter.

Abstract

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 $\Big(\frac{2+3w}{1+3w}\Big)\pi \frac{v^2}{c^2}$.