Energy in critical collapse

TL;DR

This paper investigates the energy distribution in critical scalar field collapse, revealing that material energy dominates gravitational energy and identifying key indicators like the $m/r$ ratio for apparent horizon formation.

Contribution

It provides new insights into the energy dynamics and the role of the $m/r$ ratio in critical gravitational collapse of scalar fields.

Findings

Material energy exceeds gravitational energy in critical collapse.

The maximum $m/r$ fluctuates between 2/15 and 4/15.

The $m/r$ ratio is crucial for apparent horizon formation detection.

Abstract

We study the energy issue in critical collapse of a spherically symmetric scalar field. It is found that in critical collapse, the contribution from the material energy is greater than that from the gravitational energy. The quantity $m/r$ plays an important role in identifying the formation of apparent horizon in gravitational collapse, where $m$ is the Misner-Sharp mass and $r$ the areal radius. We observe that in critical collapse, the maximum value of $m/r$ fluctuates between $2/15$ and $4/15$. This denotes a large gap between critical collapse and black hole formation for which the criterion is $m/r=1/2$.