Collapsing spherical stars in f(R) gravity

TL;DR

This paper investigates gravitational collapse in f(R) gravity, revealing that additional matching conditions impose unphysical constraints, preventing realistic collapse scenarios and affecting black hole physics and cosmic censorship.

Contribution

It demonstrates that homogeneous stars with non-constant Ricci scalar cannot be smoothly matched in f(R) gravity, and provides an exact inhomogeneous collapse solution with stability considerations.

Findings

Extra matching conditions impose unphysical constraints.

Homogeneous stars with non-constant Ricci scalar cannot be matched.

An exact inhomogeneous collapse solution is found but is unstable.

Abstract

We perform a careful investigation of the problem of physically realistic gravitational collapse of massive stars in f(R)-gravity. We show that the extra matching conditions that arise in the modified gravity imposes strong constraints on the stellar structure and thermodynamic properties. In our opinion these constraints are unphysical. We prove that no homogeneous stars with non-constant Ricci scalar can be matched smoothly with a static exterior for any nonlinear function f(R). Therefore, these extra constraints make classes of physically realistic collapse scenarios in general relativity, non-admissible in these theories. We also find an exact solution for an inhomogeneous collapsing star in the Starobinski model that obeys all the energy and matching conditions. However, we argue that such solutions are fine-tuned and unstable to matter perturbations. Possible consequences on black hole physics and the cosmic censorship conjecture are also discussed.