Trapped surfaces in Oppenheimer-Snyder black holes

TL;DR

This paper investigates the precise location of trapped surfaces within Oppenheimer-Snyder black holes, providing explicit examples and matching conditions at the boundary between collapsing dust and vacuum regions.

Contribution

It offers a detailed analysis of trapped surfaces inside Oppenheimer-Snyder black holes, including explicit examples and boundary matching techniques.

Findings

Explicit trapped spheres extending into vacuum region

Boundary of trapped region meets the center of the dust cloud

Matched solutions at the junction between dust and vacuum

Abstract

The Oppenheimer-Snyder solution models a homogeneous round dust cloud collapsing to a black hole. Inside its event horizon there is a region through which trapped surfaces pass. We try to determine exactly where the boundary of this region meets the centre of the cloud. We present explicit examples of the relevant trapped (topological) spheres; they extend into the exterior vacuum region, and are carefully matched at the junction between the cloud and the vacuum.