Stable black holes in lower dimensional $f(\mathbb{Q})$ non-metric gravity

TL;DR

This paper explores new black hole solutions in (2+1)-dimensional $f( ext{ extbf{Q}})$ gravity, revealing how quadratic non-metricity corrections alter their structure, thermodynamics, and stability compared to standard models.

Contribution

It introduces novel black hole solutions in lower-dimensional $f( ext{ extbf{Q}})$ gravity with detailed analysis of their properties and stability, extending understanding beyond General Relativity.

Findings

Quadratic corrections modify black hole geometry from BTZ solutions.

Black holes exhibit weaker singularities due to non-metricity effects.

Multi-horizon configurations are possible in this framework.

Abstract

We investigate exact charged and uncharged black hole solutions in a (2+1)-dimensional spacetime within the framework of quadratic form of $f(\mathbb{Q})$ symmetric teleparallel gravity, where $\mathbb{Q}$ is the non-metricity scalar. By adopting spherical symmetry and considering both vanishing and non-vanishing electromagnetic fields, we derive new classes of black hole solutions and analyze their geometric and physical properties. The study demonstrates that the inclusion of quadratic corrections in the gravitational Lagrangian significantly modifies the structure of solutions, producing deviations from the standard BTZ geometry. Invariants such as curvature and non-metricity scalars are calculated to classify the singularity structure and spacetime behavior. Thermodynamic quantities, including Hawking temperature, entropy, and heat capacity, are computed, showing consistency with the first law of black hole thermodynamics. Furthermore, we examine the geodesic motion of test particles and derive the effective potential to explore the stability of photon orbits. A notable outcome is the identification of weaker black hole singularities in comparison to General Relativity, attributed to the non-metricity corrections. The possibility of multi-horizon configurations is also explored. This study provides a comprehensive analysis of the gravitational, thermodynamic, and dynamical features of lower-dimensional black holes in $f(\mathbb{Q})$ gravity and highlights their distinct characteristics with respect to General Relativity.