Spherically Symmetric Space-Times in Generalized Hybrid Metric-Palatini Gravity

Abstract: We discuss vacuum static, spherically symmetric asymptotically flat solutions of the generalized hybrid metric-Palatini theory of gravity (generalized HMPG) suggested by Böhmer and Tamanini, involving both a metric (Formula presented.) and an independent connection (Formula presented.); the gravitational field Lagrangian is an arbitrary function f(R,P) of two Ricci scalars, R obtained from (Formula presented.) and P obtained from (Formula presented.). The theory admits a scalar-tensor representation with two scalars (Formula presented.) and a potential (Formula presented.) whose form depends on f(R,P). Solutions are obtained in the Einstein frame and transferred back to the original Jordan frame for a proper interpretation. In the completely studied case (Formula presented.), generic solutions contain naked singularities or describe traversable wormholes, and only some special cases represent black holes with extremal horizons. For (Formula presented.), some examples of analytical solutions are obtained and shown to possess naked singularities. Even in the cases where the Einstein-frame metric (Formula presented.) is found analytically, the scalar field equations need a numerical study, and if (Formula presented.) contains a horizon, in the Jordan frame it turns to a singularity due to the corresponding conformal factor. © 2021, Pleiades Publishing, Inc.