Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity

Abstract: Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the second-order corrections of general relativity, namely, $R^{2}$, $R^{3}$ and $R\square R$. Then, we explore spherically symmetric and static solutions in the weak-field regime and black holes context. All solutions in the weak-field regime due to a point mass are deduced, and by making a stability analysis of these solutions, we restrict them to Yukawa-type solutions. In regard to black hole solutions, we use the Lichnerovicz method to investigate the possibility of existence of non-Schwarzschild black holes. The results obtained show that non-Schwarzschild solutions might exist. However, for reasonable values of the parameters of the theory, its horizon radii are extremely small making macroscopic black holes different from Schwarzschild unfeasible.