The lightlike geometry of marginally trapped surfaces in Minkowski space-time

TL;DR

This paper explores the lightlike geometric properties of marginally trapped surfaces in Minkowski space-time, extending Lorentzian differential geometry concepts to analyze these special spacelike submanifolds.

Contribution

It introduces a detailed study of marginally trapped surfaces using lightlike geometry, expanding the understanding of their structure in Lorentz-Minkowski space.

Findings

Characterization of marginally trapped surfaces via lightlike geometry

Extension of Lorentzian differential geometry methods

New insights into the structure of spacelike submanifolds in Minkowski space

Abstract

The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we investigate a special class of surfaces (i.e., marginally trapped surfaces) in Minkowski space-time from the view point of the lightlike geometry.