Critical collapse for the Starobinsky $R^2$ model

TL;DR

This paper investigates gravitational collapse in the Starobinsky $R^2$ model, revealing how black holes form and analyzing critical phenomena near the threshold, with a focus on the Einstein frame representation.

Contribution

It provides the first detailed analysis of critical collapse in the $f(r)$ gravity model, specifically the Starobinsky $R^2$ model, including threshold determination and scalar field dynamics.

Findings

Black hole formation occurs via scalar field collapse in the $R^2$ model.

Critical collapse behavior is characterized near the black hole formation threshold.

The Schwarzschild metric emerges as the end state in collapsing scenarios.

Abstract

We study gravitational collapse for the Starobinsky $R^2$ model, a particular example of an $f(r)$ theory, in a spherically symmetric spacetime. We add a massless scalar field as matter content to the spacetime. We work in the Einstein frame, where an additional scalar field arises due to the conformal transformation. As in general relativity, depending on the initial data, we found that the gravity scalar field and the physical scalar field can collapse, forming a black hole, in which the final solution is the Schwarzschild metric. We found the threshold of black hole formation through a fine-tuning method and studied critical collapse near this regime.