LAUSR

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 gμν and an independent connection Γ̂ α μν ; the gravitational field Lagrangian is an arbitrary function f(R,P ) of two Ricci scalars, R obtained from gμν and P obtained from Γ̂ α μν . The theory admits a scalartensor representation with two scalars φ and ξ and a potential V (φ, ξ) 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 V ≡ 0, generic solutions contain naked singularities or describe traversable wormholes, and only some special cases represent black holes with extremal horizons. For V (φ, ξ) 6= 0, some examples of analytical solutions are obtained and shown to possess naked singularities. Even in the cases where the Einstein-frame metric g μν is found analytically, the scalar field equations need a numerical study, and if g μν contains a horizon, in the Jordan frame it turns to a singularity due to the corresponding conformal factor.