Junction conditions for generalized hybrid metric-Palatini gravity with applications

The generalized hybrid metric-Palatini gravity is a theory of gravitation that has an action composed Lagrangian given by $f(R,\mathcal{R})$, where $f$ function the metric Ricci scalar $R$ and new $\mathcal{R}$ formed from Palatini connection, plus matter Lagrangian. This can be rewritten trading geometric degrees freedom appear in $f(R,\mathcal{R})$ into two fields, $\ensuremath{\varphi}$ $\ensuremath{\psi}$, yielding dynamically equivalent scalar-tensor theory. Given spacetime theory, next important step to find solutions within it. To construct appropriate it often necessary know junction conditions between regions at separation hypersurface $\mathrm{\ensuremath{\Sigma}}$, with each region being independent solution for are found here, both representation representation, addition, matching thin-shell smooth worked out. These then applied three configurations, namely, star, quasistar black hole, wormhole. star made Minkowski interior, thin shell interface all energy satisfied, Schwarzschild exterior mass $M$, unlike general relativity performed any radius ${r}_{\mathrm{\ensuremath{\Sigma}}}$, this only specific value radius, namely ${r}_{\mathrm{\ensuremath{\Sigma}}}=\frac{9M}{4}$, corresponds relativistic Buchdahl radius. hole interior surrounded thick matches smoothly $M$ light ring ${r}_{\mathrm{\ensuremath{\Sigma}}e}=3M$, satisfied whole spacetime. wormhole some contains throat, interface, Schwarzschild-AdS negative cosmological constant $\mathrm{\ensuremath{\Lambda}}$, null condition obeyed everywhere