Junction conditions of Palatini $f\left(\mathcal{R},T\right)$ gravity

Abstract

We work out the junction conditions for the Palatini $f(\mathcal{R},T)$ extension of General Relativity, where $f$ is an arbitrary function of the curvature scalar $\mathcal{R}$ of an independent connection, and of the trace $T$ of the stress-energy tensor of the matter fields. We find such conditions on the allowed discontinuities of several geometrical and matter quantities, some of which depart from their metric counterparts, and in turn extend their Palatini $f(\mathcal{R})$ versions via some new $T$-dependent terms. Moreover, we also identify some "exceptional cases" of $f(\mathcal{R},T)$ Lagrangians such that some of these conditions can be discarded, thus allowing for further discontinuities in $\mathcal{R}$ and $T$ and, in contrast with other theories of gravity, they are shown to not give rise to extra components in the matter sector e.g. momentum fluxes and double gravitational layers. We discuss how these junction conditions, together with the non-conservation of the stress-energy tensor ascribed to these theories, may induce non-trivial changes in the shape of specific applications such as traversable thin-shell wormholes.

11 pages

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• Extended Tolman III and VII solutions in $f(\mathcal{R},T)$ gravity: Models for neutron stars and supermassive stars
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• Energy-Momentum Squared Gravity: A Brief Overview
• Traversable wormholes with double layer thin shells in quadratic gravity
• Junction conditions in gravity theories with extra scalar degrees of freedom
• On the visibility of singularities in general relativity and modified gravity theories
• Junction conditions in bi-scalar Poincaré Gauge gravity
• Multiway Junction Conditions: Booklets and Webs
• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Scalar-tensor representation to $f(R,T)-$brane with Gauss-Bonnet gravity