On the junction conditions in $f(R)$-gravity with torsion

TL;DR

This paper derives and discusses junction conditions in $f(R)$-gravity with torsion, highlighting differences from Einstein--Cartan theory, especially when coupled to Dirac fields and spin fluids.

Contribution

It provides the first detailed derivation of junction conditions in $f(R)$-gravity with torsion, including specific cases of matter coupling.

Findings

General junction conditions derived for $f(R)$-gravity with torsion

Explicit treatment of Dirac field and spin fluid couplings

Differences from Einstein--Cartan--Sciama--Kibble theory outlined

Abstract

Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with respect to Einstein--Cartan--Sciama--Kibble theory $\left(f(R)=R\right)$ are outlined.