On the mechanism of trapped surface formation

TL;DR

This paper investigates the formation of trapped surfaces in spherical stars using analytical and numerical methods, revealing conditions for apparent horizon locations and criteria for trapped region presence based on density profiles.

Contribution

It introduces a new criterion linking density and radius to predict trapped surface formation in spherical stars.

Findings

Inner apparent horizon lies within or at the star's surface.

Outer apparent horizon can exist in vacuum with non-zero ADM mass.

Trapped surfaces in non-decreasing density profiles form on a thick shell.

Abstract

By a combination of analytical and numerical methods, the density profile of a momentarily at rest spherical star is varied, and the corresponding response in the area of the spherical shells is monitored. It is shown that the inner apparent horizon (if it exists) must lie within or at most on the star's surface, while no such restriction is found for the outer apparent horizon. However, an apparent horizon lying in the vacuum region will always have non vanishing area, as long as the ADM mass of the system is non zero. Furthermore for density profiles not decreasing inwards, it appears that all spherical trapped surfaces lie on a thick spherical shell. Finally for a uniform density star a simple criterion is found, relating density and proper radius that guarantees the presence or absence of trapped regions.