Junction conditions for generalized hybrid metric-Palatini gravity with applications

Abstract

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

26 pages, 3 figures

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• Junction conditions of Palatini $f\left(\mathcal{R},T\right)$ gravity
• Traversable wormholes with double layer thin shells in quadratic gravity
• Junction conditions in gravity theories with extra scalar degrees of freedom
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• On the visibility of singularities in general relativity and modified gravity theories
• Multiway Junction Conditions: Booklets and Webs
• Junction conditions in bi-scalar Poincaré Gauge gravity
• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Gravitational wave propagation in generalized hybrid metric-Palatini gravity
• Dark energy from a geometrical gauge scalar-tensor theory of gravity
• Sculpting Spacetime: Thin Shells in Wormhole Physics