Classification of spacelike surfaces in spacetime

2007/03/22 by José M M Senovilla · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Noncommutative and Quantum Gravity Theories #gr-qc #math.DG

paper · pdf · doi:10.1088/0264-9381/24/11/020

published as Class.Quant.Grav.24:3091-3124,2007 · 42 pages, 10 tables, many diagrams

arxiv created 2007/03/22 · openalex publication_date 2007/05/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

A classification of two-dimensional surfaces embedded 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.

Citations

• Singularity Theorems and Their Consequences
• Trapped surfaces, horizons and exact solutions in higher dimensions
• The singularities of gravitational collapse and cosmology

Cited by

• INVOLUTE, MINIMAL, OUTER AND INCREASINGLY TRAPPED SURFACES
• A reformulation of the hoop conjecture