Special N-dimensional charged anti-de-Sitter black holes in f(Q) gravitational theory

Abstract

In this study, we introduce a toroidal solution for charged anti-de Sitter black holes in N dimensions within the framework of the quadratic form of $f\left(Q\right)$ gravity, employing the coincident gauge condition [1]. We assume $f\left(Q\right)$ to take the form $f\left(Q\right)=Q+\frac{1}{2}\alpha Q^2-2\Lambda$, where $N\ge 4$. These black hole solutions are characterized by flat or cylindrical horizons. A notable feature of these solutions is the presence of both electric monopole and quadrupole components in the potential field. These monopole and quadrupole components are inseparable and exhibit interconnected momenta, distinguishing them from the known charged solutions in the linear case of non-metricity theory. Furthermore, we demonstrate that the curvature singularities of these solutions are less severe than those in charged general relativity solutions. Finally, we calculate thermodynamic parameters, including entropy, Hawking temperature, and Gibbs free energy. These calculations confirm the stability of our model.