Non-Riemannian Gravity and the Einstein-Proca System

TL;DR

This paper shows how solutions from Einstein-Maxwell and Einstein-Proca theories can be adapted to generate a broad class of solutions in non-Riemannian gravity theories involving torsion and non-metricity.

Contribution

It introduces a method to extend known Einstein-Maxwell and Einstein-Proca solutions to non-Riemannian gravity models with additional geometric features.

Findings

Existing solutions can be used to generate new non-Riemannian solutions.

The approach broadens the solution space of non-Riemannian gravity theories.

Connections between Riemannian and non-Riemannian solutions are established.

Abstract

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.