Spherically Symmetric Solutions in Macroscopic Gravity

TL;DR

This paper derives spherically symmetric solutions within Macroscopic Gravity, showing that averaging inhomogeneities can explain galactic rotation curves without dark matter.

Contribution

It introduces a non-perturbative, covariant averaging approach to extend Schwarzschild solutions, offering an alternative explanation for galactic dynamics.

Findings

Averaged solutions can mimic dark matter effects.

Inhomogeneities influence gravitational fields significantly.

Dark matter effects may result from averaging inhomogeneities.

Abstract

Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.