Gravitational collapse of massless scalar field in $f(R)$ gravity

TL;DR

This paper investigates how the additional scalar field in $f(R)$ gravity influences the gravitational collapse of a massless scalar field, revealing complex dynamics and conditions for black hole formation.

Contribution

It introduces the effect of the conformally transformed scalar field in $f(R)$ gravity on gravitational collapse dynamics and black hole formation.

Findings

The new scalar field adds a competing force in collapse dynamics.

Tuning initial perturbations controls the collapse outcome.

Rich physics observed in black hole formation processes.

Abstract

We study the spherically symmetric gravitational collapse of massless scalar matter field in asymptotic flat spacetime in $f(R)$ gravity. In the Einstein frame of $f(R)$ gravity, an additional scalar field arises due to the conformal transformation. We find that besides the usual competition between gravitational energy and kinetic energy in the process of gravitational collapse, the new scalar field brought by the conformal transformation adds one more competing force in the dynamical system. The dynamical competition can be controlled by tuning the amplitudes of the initial perturbations of the new scalar field and the matter field. To understand the physical reasons behind these phenomena, we analyze the gravitational potential behavior and calculate the Ricci scalar at center with the change of initial amplitudes of perturbations. We find rich physics on the formation of black holes through gravitational collapse in $f(R)$ gravity.