Spherically symmetric solution in quadratic non-metricity gravity

TL;DR

This paper presents an exact spherically symmetric solution in quadratic non-metricity gravity, revealing that the quadratic term functions as a cosmological constant and challenging previous claims about the absence of such solutions.

Contribution

The authors explicitly derive a spherically symmetric solution in quadratic non-metricity gravity, demonstrating its properties and its independence from charge effects, contradicting prior literature.

Findings

Quadratic non-metricity acts as a cosmological constant.

Explicit spherically symmetric solution found.

Charged and uncharged solutions are identical in this context.

Abstract

We explicitly find an exact spherically symmetric solution in quadratic non-metricity gravity. We show that the quadratic term acts as a cosmological constant. This solution contradicts all the claims in the literature that there is no spherically symmetric solution for higher-order non-metricity gravity. Moreover, we demonstrate that for the charged field equations, the solution can be identical to the non-charged case. This is because the off-diagonal components of the field equation do not feel the effect of the charge.