A Note on trapped Surfaces in the Vaidya Solution

TL;DR

This paper investigates the conditions under which closed trapped surfaces can extend into the flat region in the Vaidya solution, revealing that in self-similar collapse, this extension depends on the rate of mass function increase.

Contribution

It provides a specific criterion for the existence of trapped surfaces in flat regions during self-similar Vaidya collapse, clarifying a longstanding question.

Findings

Closed trapped surfaces can extend into flat regions in self-similar collapse.

Extension depends on the mass function rising sufficiently fast.

The result clarifies the geometric structure of trapped surfaces in Vaidya spacetimes.

Abstract

The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question whether closed trapped surfaces can extend into the flat region (whereas closed outer trapped surfaces certainly can). For the special case of self-similar collapse we show that the answer is yes, if and only if the mass function rises fast enough.