Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
arXiv:0901.2052 · doi:10.1103/PhysRevD.79.124010
Abstract
We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the isolated horizon formalism for black hole excision, we especially solve the non-conformally flat part of the equations, and assess the boundary condition problem for this part. In the stationary single black hole case, we present and justify a no-boundary treatment on the black hole horizon. We compare the data obtained with the well-known analytic Kerr solution in Kerr-Schild coordinates, and assess the widely used conformally flat approximation for simulating axisymmetric black hole spacetimes. Our method shows good concordance on physical and geometrical issues, with the particular application of the isolated horizon multipolar analysis to confirm that the solution obtained is indeed the Kerr spacetime. Finally, we discuss a previous suggestion in the literature for the boundary conditions for the conformal geometry on the horizon.
arXiv comment15 pages, 5 figures. Part IV significantly expanded, and additional appendix included. Version coherent with the published paper
References in corpus (48)
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Isolated and dynamical horizons and their applications
- General Laws of Black-Hole Dynamics
- A simple construction of initial data for multiple black holes
- Dynamical Horizons and their Properties
- A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity
- Introduction to Isolated Horizons in Numerical Relativity
- Black hole boundaries
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Spectral Methods for Numerical Relativity
- Isolated Horizons: A Generalization of Black Hole Mechanics
- Excision boundary conditions for black hole initial data
- Binary black-hole evolutions of excision and puncture data
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Multipole Moments of Isolated Horizons
- Binary black holes in circular orbits. I. A global spacetime approach
- Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
- Circular orbits and spin in black-hole initial data
- Introduction to dynamical horizons in numerical relativity
- Waveless Approximation Theories of Gravity
- Nonexistence of conformally flat slices of the Kerr spacetime
- Corotating and irrotational binary black holes in quasi-circular orbits
- Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method
- Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
- An explicit harmonic code for black-hole evolution using excision
- New conformally flat initial data for spinning black holes
- The Evolution of Distorted Rotating Black Holes III: Initial Data
- A generalized Damour-Navier-Stokes equation applied to trapping horizons
- Pseudo-spectral apparent horizon finders: an efficient new algorithm
- Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
- On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations
- Area evolution, bulk viscosity and entropy principles for dynamical horizons
- Binary neutron stars: Equilibrium models beyond spatial conformal flatness
- An intrinsic characterization of the Kerr metric
- Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
- Dark Matter Accretion into Supermassive Black Holes
- On the existence of initial data containing isolated black holes
- A new spectral apparent horizon finder for 3D numerical relativity
- Rotating star initial data for a constrained scheme in numerical relativity
- Numerical implementation of isolated horizon boundary conditions
- Kerr Initial data
- Trapping Horizons as inner boundary conditions for black hole spacetimes
- Isolated Horizon structures in quasiequilibrium black hole initial data
- On the boundary of the region containing trapped surfaces
Cited by in corpus (14)
- Kadath: a spectral solver for theoretical physics
- Spacetime near isolated and dynamical trapping horizons
- The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis
- Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes
- An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
- Collapse of differentially rotating supermassive stars: Post black hole formation
- Initial data for perturbed Kerr black holes on hyperboloidal slices
- A new method to compute quasi-local spin and other invariants on marginally trapped surfaces
- Quasi-Local Black Hole Horizons: Recent Advances
- Complete initial value spacetimes containing black holes in general relativity: Application to black hole-disk systems
- An excision scheme for black holes in constrained evolution formulations: spherically symmetric case
- A spectral method for the wave equation of divergence-free vectors and symmetric tensors inside a sphere
- A Black-Hole Excision Scheme for General Relativistic Core-Collapse Supernova Simulations
- Boundary conditions for stationary black holes ; Application to Kerr, Martinez-Troncoso-Zanelli and hairy black holes