Maxwell- f ( Q ) $f(Q)$ Theory

Exploring the four-dimensional AdS black hole is crucial within the framework of the AdS/CFT correspondence. In this research, four-dimensional stationary and rotating AdS solutions in the framework of the $f\left(Q\right)$ gravitational theory are investigated, considering the charged scenario. Author's emphasis is on the power-law ansatz, which 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. The singularities of such a solution are analyzed, computing all the quantities of different curvature and non-metricity invariants. Author's 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 $f\left(Q\right)$. Several physical characteristics of black hole from thermodynamics perspective and demonstrate the existence of an outer event horizon in addition to the inner Cauchy horizons are examined. However, under the conditions of sufficiently large electric charge, a naked singularity emerges. Finally, a class of rotating black hole in four-dimensional $f\left(Q\right)$ gravity that are asymptotically anti-de Sitter charged is derived.