Junction conditions in Palatini $f(R)$ gravity

TL;DR

This paper derives the junction conditions for Palatini $f(R)$ gravity, highlighting differences from General Relativity, and demonstrates their implications for modeling stellar surfaces like neutron stars and white dwarfs.

Contribution

It provides the first detailed derivation of junction conditions in Palatini $f(R)$ gravity using a tensor distributional approach, revealing key differences from GR.

Findings

Trace of stress-energy tensor must be continuous across hypersurface

Normal derivative of stress-energy tensor need not be continuous

Neutron stars and white dwarfs can be modeled within Palatini $f(R)$ gravity

Abstract

We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of General Relativity and from their metric $f(R)$ counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need not to. We illustrate the relevance of these conditions by considering the properties of stellar surfaces in polytropic models, showing that the range of equations of state with potentially pathological effects is shifted beyond the domain of physical interest. This confirms, in particular, that neutron stars and white dwarfs can be safely modelled within the Palatini $f(R)$ framework.