Marginally trapped surfaces in null normal foliation spacetimes: A one step generalization of LRS II spacetimes

Abstract

In this paper, we study geometrical properties of marginally trapped surfaces in gravitational collapse, using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables. We first define a generalization (in a sense to be specified in the introduction) of LRS II spacetime — which we call NNF spacetimes — and show that the marginally trapped surfaces in NNF spacetimes (and the 3-surfaces they foliate) are topologically equivalently those of LRS II spacetimes. We then study the evolution of MTTs (3-surfaces foliated by marginally trapped surfaces), extending earlier work on LRS II spacetimes to NNF spacetimes, and in general any 4-dimensional spacetime. In addition, we perform a stability analysis for the marginally trapped surfaces in this formalism, using simple spacetimes as examples to demonstrate the applicability of our approach.