Horizon structure and extremal configurations of Kerr-Newman-anti-de Sitter black holes in f(R) gravity
Exploiting the correspondence between Kerr--Newman--(A)dS black hole solutions in general relativity and their constant-curvature counterparts in $f(R)$ gravity, we employ a unified framework to investigate the horizon structure and extremal configurations of these black holes, focusing primarily on the anti--de Sitter case. By solving the extremality conditions with respect to the squared rotation parameter $a^2$ and the inverse curvature scale $l^{-2}$, we obtain closed analytic relations that provide a transparent parametrization of the extremal branch in the $(a^2,\, l^{-2})$ parameter space. We determine the physically admissible domain of the rotating extremal branch and derive the corresponding critical charge, $q_{\max}=M/2$, at which the metric becomes singular and the branch reaches its critical rotation limit. For vanishing electric charge, the rotation parameter decreases monotonically along the extremal branch and remains bounded from below, implying the existence of a minimal rotation, $a_{\min}=3\sqrt{3}M/8$. The rotating extremal branch also exhibits a distinguished internal point at which the normalized rotational and curvature scales coincide. The inclusion of electric charge introduces an additional competing scale, broadening the rotating extremal branch while lowering the corresponding minimal rotation to $a_{\min}=M/4$ at the critical charge $q_{\max}=M/2$. Comparing these results with the corresponding de Sitter case, we show that extremality in AdS is constrained by a geometric endpoint, whereas the dS branch exhibits a considerably richer structure characterized by an ultra-extremal maximum and a subsequent decay toward the non-rotating limit. Finally, we demonstrate that the algebraic mass constraint associated with the quartic horizon equation completely removes the real-root structure, yielding a class of solutions without physical horizons.