Maxwell-$f(Q)$ theory

TL;DR

This paper investigates four-dimensional charged and rotating AdS black hole solutions within the novel $f(Q)$ gravity framework, analyzing their singularities, horizons, thermodynamics, and the impact of non-metricity and Maxwell fields.

Contribution

It introduces a new class of charged and rotating AdS black hole solutions in $f(Q)$ gravity, highlighting features distinct from general relativity and exploring their physical properties.

Findings

Presence of a central singularity with softer characteristics than in GR.

Existence of outer event and inner Cauchy horizons under certain conditions.

Emergence of naked singularities at high electric charges.

Abstract

Exploring the four-dimensional AdS black hole is crucial within the framework of the AdS/CFT correspondence. In this research, considering the charged scenario, we investigate the four-dimensional stationary and rotating AdS solutions in the framework of the $f(Q)$ gravitational theory. Our emphasis is on the power-law ansatz, which is consistent with observations and is deemed the most viable. Because this solution does not have an uncharged version or relate to general relativity, it falls into a new category, which derives its features from changes in non-metricity and incorporates the Maxwell domain. We analyze the singularities of such a solution, computing all the quantities of different curvature and non-metricity invariants. Our results indicate the presence of a central singularity, albeit with a softer nature compared to standard non-metricity or Einstein general relativity, attributed to the influence of the effect of $f(Q)$. We examine several physical characteristics of black holes from a thermodynamics perspective and demonstrate the existence of an outer event horizon in addition to the inner Cauchy horizons. However, under the conditions of a sufficiently large electric charge, a naked singularity emerges. Finally, we derive a class of rotating black hole in four-dimensional $f(Q)$ gravity that are asymptotically anti-de Sitter charged.