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

TL;DR

This paper derives the junction conditions for Palatini $f(\,\mathcal{R},T)$ gravity, revealing how discontinuities in geometrical and matter quantities differ from metric theories and exploring implications for exotic structures like wormholes.

Contribution

It extends the junction conditions framework to Palatini $f(\,\mathcal{R},T)$ gravity, including new $T$-dependent terms and exceptional cases allowing additional discontinuities.

Findings

Derived junction conditions for Palatini $f(\,\mathcal{R},T)$ gravity.

Identified cases where discontinuities are permitted without extra matter components.

Discussed implications for traversable thin-shell wormholes.

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.