Optical scalars in spherical spacetimes

TL;DR

This paper derives universal bounds for optical scalars in spherically symmetric spacetimes under certain energy and regularity conditions, aiding in understanding apparent horizon formation.

Contribution

It introduces a universal bound for optical scalars applicable to various matter distributions in spherical spacetimes, including singular cases.

Findings

Bound applies to matter satisfying dominant energy condition

Bounds hold for shells and conical singularities

Provides new criteria for apparent horizon formation

Abstract

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant energy condition and that the slice be asymptotically flat and regular at the origin. This bound can be used to derive new conditions for the formation of apparent horizons. The bounds hold even when the matter has a distribution on a shell or blows up at the origin so as to give a conical singularity.