3-dimensional charged black holes in $f({Q})$ gravity

TL;DR

This paper introduces new exact charged black hole solutions in (2+1) dimensions within $f(Q)$ gravity, revealing unique features like multiple horizons, stable photon orbits, and thermodynamic stability, driven by higher-order non-metricity effects.

Contribution

It provides the first explicit charged black hole solutions in $f(Q)$ gravity with a cubic form, including a novel solution not deformable from GR, and analyzes their geometrical and thermodynamic properties.

Findings

Existence of multiple horizons in the solutions.

Discovery of a novel asymptotically AdS charged black hole not deformable from GR.

Thermodynamic analysis shows thermal stability of the solutions.

Abstract

We present new exact charged black hole solutions in (2+1) dimensions within the framework of $f({Q})$ gravity, where ${Q}$ denotes the non-metricity scalar. By considering a cubic $f({Q})$ form we derive classes of charged and uncharged spherically symmetric solutions, and we identify conditions under which these reduce to the well-known Banados-Teitelboim-Zanelli (BTZ) black hole. Notably, our analysis reveals a novel charged solution that is asymptotically Anti-de Sitter (AdS) but cannot be continuously deformed into a GR counterpart, and thus arising purely from the higher-order nature of the non-metricity corrections. Furthermore, we explore the geometrical properties of the solutions, demonstrating the existence of multiple horizons and a softer central singularity compared to GR. Additionally, we calculate various thermodynamic quantities, such as Hawking temperature, entropy, and heat capacity, with results confirming thermal stability. Finally, a detailed study of the geodesic motion and the effective potentials unveils stable photon orbits, as well as the effect of cubic non-metricity corrections on orbital dynamics.