Symmetric non-expanding horizons

Abstract

Symmetric non-expanding horizons are studied in arbitrary dimension. The global properties -as the zeros of infinitesimal symmetries- are analyzed particularly carefully. For the class of NEH geometries admitting helical symmetry a quasi-local analog of Hawking's rigidity theorem is formulated and proved: the presence of helical symmetry implies the presence of two symmetries: null, and cyclic. The results valid for arbitrary-dimensional horizons are next applied in a complete classification of symmetric NEHs in 4-dimensional space-times (the existence of a 2-sphere crossection is assumed). That classification divides possible NEH geometries into classes labeled by two numbers - the dimensions of, respectively, the group of isometries induced in the horizon base space and the group of null symmetries of the horizon.

Revtex4, 36 pages

References in corpus (37)

• A rotating black ring in five dimensions
• Isolated and dynamical horizons and their applications
• General Laws of Black-Hole Dynamics
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Dynamical Horizons and their Properties
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Generic Isolated Horizons and their Applications
• Mechanics of Rotating Isolated Horizons
• Black hole boundaries
• Dynamic black-hole entropy
• Geometry of Generic Isolated Horizons
• Mechanics of Isolated Horizons
• Isolated Horizons: A Generalization of Black Hole Mechanics
• The first law for slowly evolving horizons
• Energy and entropy conservation for dynamical black holes
• Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri
• A boundary value problem for the five-dimensional stationary rotating black holes
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• Extremal Isolated Horizons: A Local Uniqueness Theorem
• Energy conservation for dynamical black holes
• Space-Times Admitting Isolated Horizons
• Spin-Coefficient Form of the New Laws of Black-Hole Dynamics
• Quasi-local rotating black holes in higher dimension: geometry
• Quasi-local first law of black-hole dynamics
• Mechanics of multidimensional isolated horizons
• Horizon energy and angular momentum from a Hamiltonian perspective
• Metric-based Hamiltonians, null boundaries, and isolated horizons
• Spacetimes foliated by Killing horizons
• Geometric Characterizations of the Kerr Isolated Horizon
• Uniqueness theorem for stationary black hole solutions of σ-models in five dimensions
• Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description
• Boundary Terms and Noether Current of Sphereical Black Holes
• Gravitational radiation from dynamical black holes
• Dynamics of gravitational field within a wave front and thermodynamics of black holes
• Intrinsic Geometry of a Null Hypersurface
• Geometry of null hypersurfaces
• Local approach to thermodynamics of black holes

Cited by in corpus (20)

• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Black holes and black hole thermodynamics without event horizons
• Charges and Fluxes on (Perturbed) Non-expanding Horizons
• The spacetime in the neighborhood of a general isolated black hole
• Non-Expanding horizons: Multipoles and the Symmetry Group
• Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition
• Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric
• Local version of the no-hair theorem
• Multiple Killing Horizons
• The Petrov type D isolated null surfaces
• Neighbourhoods of Isolated Horizons and their stationarity
• Some spacetimes containing non-rotating extremal isolated horizons
• Vacuum non-expanding horizons and shear-free null geodesic congruences
• Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes
• Non-singular Kerr-NUT-de Sitter spacetimes
• Kerr Isolated Horizons in Ashtekar and Ashtekar-Barbero Connection Variables
• Petrov type D equation on horizons of nontrivial bundle topology
• Initial data for a deformed isolated horizon
• On Super-Translation transition between Quasi-local Black holes
• Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $>0$