A numeric solution for metric-affine gravity and Einstein's gravitational theory with Proca matter

TL;DR

This paper presents a numerical solution in metric-affine gravity that models a static, spherically symmetric spacetime with Proca matter, revealing a naked singularity without an event horizon, thus connecting MAG to Einstein's gravity.

Contribution

It provides a detailed numerical solution for a Reissner-Nordström type spacetime in metric-affine gravity with Proca matter, highlighting the existence of a naked singularity.

Findings

Solution is static and spherically symmetric

No horizon exists, leading to a naked singularity

Connects metric-affine gravity to Einstein's theory with Proca matter

Abstract

A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordstr"om type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity as its origin.