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

We discuss vacuum static, spherically symmetric asymptotically flat solutions of the generalized hybrid metric-Palatini theory gravity (generalized HMPG) suggested by Böhmer and Tamanini, involving both a metric $$g_{\mu\nu}$$ an independent connection $$\hat{\Gamma}_{\mu\nu}^{\alpha}$$ ; gravitational field Lagrangian is arbitrary function $$f(R,P)$$ two Ricci scalars, $$R$$ obtained from $$P$$ $${\hat{\Gamma}}_{\mu\nu}^{\alpha}$$ . The admits scalar-tensor representation with scalars $$\phi$$ $$\xi$$ potential $$V(\phi,\xi)$$ whose form depends on Solutions are in Einstein frame transferred back to original Jordan for proper interpretation. In completely studied case $$V\equiv 0$$ , generic contain naked singularities or describe traversable wormholes, only some special cases represent black holes extremal horizons. For $$V(\phi,\xi)\neq examples analytical shown possess singularities. Even where Einstein-frame $$g^{E}_{\mu\nu}$$ found analytically, scalar equations need numerical study, if contains horizon, it turns singularity due corresponding conformal factor.