Is gravitational collapse possible in $f(R)$ gravity?

TL;DR

This paper investigates gravitational collapse within $f(R)$ gravity, revealing that traditional models like Oppenheimer-Snyder are incompatible with certain $f(R)$ formulations and presenting new exterior solutions.

Contribution

It generalizes the Oppenheimer-Snyder collapse model to $f(R)$ gravity, discovers new exterior vacuum solutions, and shows incompatibility of the model with Palatini $f(R)$ gravity.

Findings

Oppenheimer-Snyder model incompatible with metric $f(R)$ gravity.

New vacuum exterior solutions for $f(R)$ gravity are found.

Oppenheimer-Snyder collapse incompatible with Palatini $f(R)$ gravity.

Abstract

Gravitational collapse is still poorly understood in the context of $f(R)$ theories of gravity, since the Oppenheimer-Snyder model is incompatible with their junction conditions. In this work, we will present a systematic approach to the problem. Starting with a thorough analysis of how the Oppenheimer-Snyder construction should be generalised to fit within metric $f(R)$ gravity, we shall subsequently proceed to explore the existence of novel exterior solutions compatible with physically viable interiors. Our formalism has allowed us to show that some paradigmatic vacuum metrics cannot represent spacetime outside a collapsing dust star in metric $f(R)$ gravity. Moreover, using the junction conditions, we have found a novel vacuole solution of a large class of $f(R)$ models, whose exterior spacetime is documented here for the first time in the literature as well. Finally, we also report the previously unnoticed fact that the Oppenheimer-Snyder model of gravitational collapse is incompatible with the Palatini formulation of $f(R)$ gravity.