Black hole solutions in scalar-tensor symmetric teleparallel gravity

TL;DR

This paper explores exact scalarized black hole solutions in symmetric teleparallel gravity with nonmetricity, revealing analogues of known solutions and new scalarized configurations, along with no-hair theorems and implications for $f(Q)$ gravity.

Contribution

It introduces exact scalarized black hole solutions in symmetric teleparallel scalar-tensor theories, including analogues of known solutions and new configurations not seen in other frameworks.

Findings

Existence of symmetric teleparallel analogues of known black hole solutions.

Discovery of new scalarized black hole configurations.

Derivation of no-hair theorems and reduction of $f(Q)$ gravity to GR under certain conditions.

Abstract

Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include $f(Q)$ gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other ($g_{rr}=1/g_{tt}$), the $f(Q)$ gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.