Exact black hole solutions with a conformally coupled scalar field and dynamic Ricci curvature in f(R) gravity theories

We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field $f(R)$ gravity. first consider the model $f(R) = R -2\alpha \sqrt{R}$ and derive an solution. Then, we =R -2 \Lambda \alpha \sqrt{R-4 }$ In both cases modified gravity parameter $\alpha$, which has dimension of inverse mass, cannot be set to zero potential is determined from Klein-Gordon equation, preserving conformal invariance. The thermodynamics also studied.