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Novel static black hole solutions with electric and magnetic charges arederived for the class of modified gravities: $f({\cal R})={\calR}+2\beta\sqrt{{\cal R}}$, with or without a cosmological constant. The newblack holes behave asymptotically as flat or (A)dS space-times with a dynamicalvalue of the Ricci scalar given by $R=\frac{1}{r^2}$ and$R=\frac{8r^2\Lambda+1}{r^2}$, respectively. They are characterized by threeparameters, namely their mass and electric and magnetic charges, and constituteblack hole solutions different from those in Einstein's general relativity.Their singularities are studied by obtaining the Kretschmann scalar and Riccitensor, which shows a dependence on the parameter $\beta$ that is not permittedto be zero. A conformal transformation is used to display the black holes inEinstein's frame and check if its physical behavior is changed w.r.t. theJordan one. The thermal stability of the solutions is discussed by usingthermodynamical quantities, in particular the entropy, the Hawking temperature,the quasi-local energy, and the Gibbs free energy. Also, the casual structureof the new black holes is studied, and a stability analysis is performed inboth frames using the odd perturbations technique and the study of the geodesicdeviation. It is concluded that, generically, there is coincidence of thephysical properties of the novel black holes in both frames, although thisturns not to be the case for the Hawking temperature.

european physical journal. c, particles and fields

Spherically symmetric black holes with electric and magnetic charge in  extended gravity: Physical properties, causal structure, and stability  analysis in Einstein's and Jordan's frames