Black Hole Topologies and Geodesic Structures in Symmetric Teleparallel f(Q) Gravity

TL;DR

This paper investigates black hole solutions in symmetric teleparallel $f(Q)$ gravity in (2+1) dimensions, analyzing their geometric, topological, and thermodynamic properties, revealing novel singularity and horizon behaviors influenced by charge and non-metricity.

Contribution

It derives exact black hole solutions in $f(Q)$ gravity, exploring their topological and geodesic structures, and examines how charge and non-metricity affect horizons and singularities.

Findings

Horizon radii increase with charge parameter.

Higher non-metricity or cosmological constant reduces horizons.

Singularities can be geodesically reachable depending on charge.

Abstract

Black hole solutions are studied here within the symmetric teleparallel formulation of gravity, employing the $f(Q)$ model in which the gravitational dynamics are governed by the non-metricity scalar $Q$. We focus on static, circularly symmetric spacetimes in $(2+1)$-dimensions, analyzing both charged and uncharged cases. By adopting a power-law form for $f(Q)$, we derive exact black hole solutions and explore their thermodynamic and geometric properties. Curvature and non-metricity scalars reveal central singularities stronger than those in general relativity. we find that the horizon radii increase with the charge parameter while higher values of the non-metricity coefficient, $c_{4}$, or the cosmological constant $\Lambda$ tend to merge or eliminate horizons, reducing their total number and altering the near-origin structure of the spacetime. We perform a detailed topological analysis based on the Euler characteristic and examine the geodesic completeness of the spacetime. Our findings show that, depending on the presence of electric charge, the singularity may or may not be reachable by geodesics. The thermodynamic stability is confirmed via temperature, entropy, and heat capacity calculations. This study highlights the rich structure of $f(Q)$ gravity in lower-dimensional settings and offers new insights into the nature of singularities and black hole topologies in modified gravity theories.