A Reformulation of the Hoop Conjecture
arXiv:0709.0695 · doi:10.1209/0295-5075/81/20004
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.
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
References in corpus (27)
- A rotating black ring in five dimensions
- Isolated and dynamical horizons and their applications
- General Laws of Black-Hole Dynamics
- Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
- Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
- Singularity Theorems and Their Consequences
- Black hole boundaries
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Instability of Ultra-Spinning Black Holes
- Local existence of dynamical and trapping horizons
- Black Rings
- Marginally trapped tubes and dynamical horizons
- On the topology and area of higher dimensional black holes
- Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
- High-energy head-on collisions of particles and hoop conjecture
- Spin-Coefficient Form of the New Laws of Black-Hole Dynamics
- Trapped surfaces and symmetries
- On rigidity of analytic black holes
- Angular momentum and an invariant quasilocal energy in general relativity
- Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop and cosmic censorship conjectures
- Isoperimetric inequality for higher-dimensional black holes
- On the Topology of Black Hole Event Horizons in Higher Dimensions
- Classification of spacelike surfaces in spacetime
- Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes
- Geometric Inequalities and Trapped Surfaces in Higher Dimensional Spacetimes
- Trapped surfaces in prolate collapse in the Gibbons-Penrose construction
- Hoop conjecture for colliding black holes : non-time-symmetric initial data
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- The 1965 Penrose singularity theorem
- Physics of Trans-Planckian Gravity
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- Black-hole production from ultrarelativistic collisions
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Critical Phenomena in Neutron Stars II: Head-on Collisions
- Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
- Thermal BEC black holes
- Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies
- Geometrical inequalities bounding angular momentum and charges in General Relativity
- Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes
- More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons
- Gravitational Instability of Exotic Compact Objects
- Geometric inequalities for black holes
- Inequality between size and angular momentum for bodies
- Birkhoff's invariant and Thorne's Hoop Conjecture
- Mathematical General Relativity
- Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture
- Formation of naked singularities in five-dimensional space-time
- Brown-York mass and the hoop conjecture in non-spherical massive systems
- On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system
- Open problems in mathematical physics
- Gravitational renormalization of quantum field theory
- Size, angular momentum and mass for objects
- Black Objects and Hoop Conjecture in Five-dimensional Space-time
- Minimum black hole mass from colliding Gaussian packets
- Notes on several phenomenological laws of quantum gravity
- On the Kalb-Ramond modified Lorentz violating hairy black holes and Thorne's hoop conjecture
- Properties of Quasi-local mass in binary black hole mergers
- Three little pieces for computer and relativity
- Primordial Black Holes: A Review of Formation and Evolution