Classification of spacelike surfaces in spacetime

Details Classification of spacelike surfaces in spacetime Classification of spacelike surfaces in spacetime

2007-03-22

arxiv.org/abs/gr-qc/0703115v1

Class.Quant.Grav.24:3091-3124,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, 10 tables, many diagrams

Scientific paper

10.1088/0264-9381/24/11/020

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.

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