Identification of black hole horizons using scalar curvature invariants

Abstract

We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.

arXiv comment52 pages

References in corpus (41)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• A rotating black ring in five dimensions
• Isolated and dynamical horizons and their applications
• Dynamical Horizons and their Properties
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Black hole boundaries
• Classification of the Weyl Tensor in Higher Dimensions
• Local existence of dynamical and trapping horizons
• A new look at the Plebanski-Demianski family of solutions
• Cosmological Multi-Black Hole Solutions
• Geometry of Generic Isolated Horizons
• Classification of near-horizon geometries of extremal black holes
• Super-energy tensors
• Extraction of Gravitational Waves in Numerical Relativity
• Alignment and algebraically special tensors in Lorentzian geometry
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• On Spacetimes with Constant Scalar Invariants
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• A spacetime characterization of the Kerr metric
• Quasi-local rotating black holes in higher dimension: geometry
• Trapped surfaces
• A novel approach to the dynamics of Szekeres dust models
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• On limits of spacetimes -- a coordinate-free approach
• Spacetime near isolated and dynamical trapping horizons
• Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
• A Note on trapped Surfaces in the Vaidya Solution
• WANDs of the Black Ring
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• On the parameters of the Kerr-NUT-(anti-)de Sitter space-time
• Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric
• Classification of Higher Dimensional Spacetimes
• Exact Event Horizon of a Black Hole Merger
• Apparent horizons in the quasi-spherical Szekeres models
• The Cartan Algorithm in Five Dimensions
• A set of invariant quality factors measuring the deviation from the Kerr metric
• Algebraic classification of five-dimensional spacetimes using scalar invariants
• Mass inflation in a D dimensional Reissner-Nordstrom black hole: a hierarchy of particle accelerators ?
• Curvature invariant characterization of event horizons of four-dimensional black holes conformal to stationary black holes
• Horizon Detection and Higher Dimensional Black Rings

Cited by in corpus (25)

• Geometric Horizons
• Action principle selection of regular black holes
• Curvature Invariants and Lower Dimensional Black Hole Horizons
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats
• Mathematical General Relativity
• Local version of the no-hair theorem
• Geometric Horizons in the Kastor-Traschen Multi Black Hole Solutions
• Suppression of spacetime singularities in quantum gravity
• Curvature Invariants for Lorentzian Traversable Wormholes
• A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function
• The axial symmetry of Kerr without the rigidity theorem
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Symmetry and instability of marginally outer trapped surfaces
• The Petrov type D equation on genus $>0$ sections of isolated horizons
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Trapped region in Kerr-Vaidya space-time
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Persistence in black hole lattice cosmological models
• Weighing the curvature invariants
• On black holes in teleparallel torsion theories of gravity
• On black holes in new general relativity
• Alternative characterization of a black hole boundary
• Black holes and their horizons in semiclassical and modified theories of gravity