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 $g_{\mu \nu }$ and an independent connection ${\hat{\Gamma }}_{\mu \nu }{}^{\alpha }$; the gravitational field Lagrangian is an arbitrary function $f(R,P)$ of two Ricci scalars, $R$ obtained from $g_{\mu \nu }$ and $P$ obtained from ${\hat{\Gamma }}_{\mu \nu }{}^{\alpha }$. The theory admits a scalar-tensor representation with two scalars $\varphi$ and $\xi$ and a potential $V(\varphi ,\xi )$ 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 $V\equiv 0$, generic solutions contain naked singularities or describe traversable wormholes, and only some special cases represent black holes with extremal horizons. For $V(\varphi ,\xi )\ne 0$, some examples of analytical solutions are obtained and shown to possess naked singularities. Even in the cases where the Einstein-frame metric $g_{\mu \nu }^E$ is found analytically, the scalar field equations need a numerical study, and if $g_{\mu \nu }^E$ contains a horizon, in the Jordan frame it turns to a singularity due to the corresponding conformal factor.

18 pages, 7 figures

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• Gravitational wave propagation in generalized hybrid metric-Palatini gravity
• Horizons, throats and bounces in hybrid metric-Palatini gravity with a non-zero potential