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We investigate static and rotating charged spherically symmetric solutions in the framework of $f({cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black hole solution has a true central singularity which is hidden behind a horizon, however for particular parameter regions it becomes a naked one. Furthermore, we investigate the thermodynamical properties of the solutions, such as the temperature, energy, entropy, heat capacity and Gibbs free energy. We extract the entropy and quasilocal energy positivity conditions, we show that negative-temperature, ultracold, black holes are possible, and we show that the obtained solutions are thermodynamically stable for suitable model parameter regions.
We investigate the solutions of black holes in $f(T)$ gravity with nonlinear power-law Maxwell field, where $T$ is the torsion scalar in teleparalelism. In particular, we introduce the Langranian with diverse dimensions in which the quadratic polynom
We systematically study the field equations of $f(mathbb Q)$ gravity for spherically symmetric and stationary metric-affine spacetimes. Such spacetimes are described by a metric as well as a flat and torsionless affine connection. In the Symmetric Te
We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance
Torsion and nonmetricity are inherent ingredients in modifications of Einteins gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsio
We study topological black hole solutions of the simplest quadratic gravity action and we find that two classes are allowed. The first is asymptotically flat and mimics the Reissner-Nordstrom solution, while the second is asymptotically de Sitter or