A reformulation of the hoop conjecture

2007/09/30 by José M. M. Senovilla, José M M. Senovilla · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Collatz conjecture #Compact space #Conjecture #Cosmology and Gravitation Theories #Dimension (graph theory) #Geometry #Mathematical analysis #Mathematics #Pure mathematics #Relativity and Gravitational Theory #Surface (topology) #gr-qc

paper · pdf · doi:10.1209/0295-5075/81/20004

published as Europhys.Lett.81:20004,2008 · 6 pages, no figures. New references included, typos corrected, explanatory comments added. Much shorter version, in order to match EPL length restrictions. To be published in EPL

arxiv created 2007/12/04 · openalex publication_date 2007/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A reformulation of the hoop conjecture based on the concept of trapped circle is presented. The problems of severe compactness in every spatial direction, and of how to superpose the hoops with the surface of the black hole, are resolved. A new conjecture concerning "peeling" properties of dynamical/trapping horizons is propounded. A novel geometric Hoop inequality is put forward. The possibility of carrying over the results to arbitrary dimension is discussed.

Citations

• Singularity Theorems and Their Consequences
• Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes
• Classification of spacelike surfaces in spacetime
• The singularities of gravitational collapse and cosmology
• Trapped surfaces in prolate collapse in the Gibbons - Penrose construction
• Formation of naked singularities: The violation of cosmic censorship
• Collapsing shells of radiation in anti–de Sitter spacetimes and the hoop and cosmic censorship conjectures
• Black holes in general relativity
• The Large Scale Structure of Space-Time
• Gravitational Collapse and Space-Time Singularities
• The existence of a black hole due to condensation of matter
• Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article
• On the topology and area of higher-dimensional black holes

Cited by

• Primordial Black Holes: A Review of Formation and Evolution
• Shape of black holes

Related

• A unified hoop conjecture for black holes and horizonless compact stars
• Birkhoff's invariant and Thorne's Hoop Conjecture
• Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture
• Shape of black holes
• Black holes