Classification of spacelike surfaces in spacetime

TL;DR

This paper presents a detailed classification scheme for 2D surfaces in spacetime based on their shape tensor properties, refining existing concepts and opening new research directions.

Contribution

It introduces a five-level classification system for spacelike surfaces in spacetime, refining concepts like trapped, umbilical, and extremal surfaces.

Findings

Refined classification of spacelike surfaces

Identification of new surface classes

Discussion of applications and research questions

Abstract

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of trapped, umbilical and extremal surfaces, which split into several different classes. The classification raises new important questions and opens many possible new lines of research. These, together with some applications and examples, are briefly considered.