Gravitational Dust Collapse in $f(R)$ Gravity

TL;DR

This paper investigates dust gravitational collapse within metric $f(R)$ gravity, deriving junction conditions and showing how constant curvature terms influence the collapse dynamics, resembling a cosmological constant effect.

Contribution

It introduces a solution for dust collapse in $f(R)$ gravity with constant scalar curvature, extending classical collapse models to modified gravity frameworks.

Findings

Constant curvature term acts like a cosmological constant.

Junction conditions are derived for interior and exterior spacetimes.

Mass calculation incorporates effects of $f(R)$ modifications.

Abstract

This paper is devoted to investigate gravitational collapse of dust in metric $f(R)$ gravity. We take FRW metric for the interior region while the Schwarzchild spacetime is considered for the exterior region of a star. The junction conditions have been derived to match interior and exterior spacetimes. The assumption of constant scalar curvature is used to find a solution of field equations. Gravitational mass is found by using the junction conditions. It is concluded that the constant curvature term $f(R_0)$ plays the role of the cosmological constant involved in the field equations of general relativity.