New rotating AdS/dS black holes in $\mathrm{f(R)}$ gravity

Abstract: It is known that general relativity (GR) theory is not consistent with the latest observations. The modified gravity of GR known as $\mathrm{f(R)}$ where $\mathrm{R}$ is the Ricci scalar, is considered to be a good candidate for dealing with the anomalies present in classical GR. In this context, we study static rotating uncharged anti-de Sitter and de Sitter (AdS and dS) black holes (BHs) using $\mathrm{f(R)}$ theory without assuming any constraints on the Ricci scalar or on $\mathrm{f(R)}$. We derive BH solutions depend on the convolution function and deviate from the AdS/dS Schwarzschild BH solution of GR. Although the field equations have no dependence on the cosmological constant, the BHs are characterized by an effective cosmological constant that depends on the convolution function. The asymptotic form of this BH solution depends on the gravitational mass of the system and on extra terms that lead to BHs being different from GR BHs but to correspond to GR BHs under certain conditions. We also investigate how these extra terms are responsible for making the singularities of the invariants milder than those of the GR BHs. We study some physical properties of the BHs from the point of view of thermodynamics and show that there is an outer event horizon in addition to the inner Cauchy horizons. Among other things, we show that our BH solutions satisfy the first law of thermodynamics. To check the stability of these BHs we use the geodesic deviations and derive the stability conditions. Finally, using the odd-type mode it is shown that all the derived BHs are stable and have a radial speed equal to one.