Energy in critical collapse

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 $m/r=1/2$.