Excision boundary conditions for the conformal metric

Abstract

Shibata, Uryū and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a freely-specifiable variable, but rather is determined as a solution to the field equations. The new set of freely-specifiable variables includes only time-derivatives of metric quantities, which makes this decomposition very attractive for the construction of quasiequilibrium solutions. To date, this new formalism has only been used for binary neutron stars. Applications involving black holes require new boundary conditions for the conformal metric on the domain boundaries. In this paper we demonstrate how these boundary conditions follow naturally from the conformal geometry of the boundary surfaces and the inherent gauge freedom of the conformal metric.

10 pages, revtex4, accepted by Physical Review D

References in corpus (25)

• Evolution of Binary Black Hole Spacetimes
• On the Numerical Integration of Einstein's Field Equations
• A simple construction of initial data for multiple black holes
• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Extrinsic Curvature and the Einstein Constraints
• Numerical Relativity and Compact Binaries
• Harmonic coordinate method for simulating generic singularities
• Excision boundary conditions for black hole initial data
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• Circular orbits and spin in black-hole initial data
• Corotating and irrotational binary black holes in quasi-circular orbits
• Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
• Uniqueness and Non-uniqueness in the Einstein Constraints
• Trapped Surfaces in Vacuum Spacetimes
• Binary neutron stars: Equilibrium models beyond spatial conformal flatness
• The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
• Vacuum Spacetimes with Future Trapped Surfaces
• Non-uniqueness in conformal formulations of the Einstein constraints
• Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
• On the existence of initial data containing isolated black holes
• Numerical implementation of isolated horizon boundary conditions
• Trapping Horizons as inner boundary conditions for black hole spacetimes
• Evolution systems for non-linear perturbations of background geometries

Cited by in corpus (8)

• Coalescence of black hole--neutron star binaries
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Status of black-hole-binary simulations for gravitational-wave detection
• General relativistic hydrodynamics in curvilinear coordinates
• Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit
• Initial data for neutron star binaries with arbitrary spins
• Isolated Horizon structures in quasiequilibrium black hole initial data
• Conformal Invariance and Phase Transitions: Implications for Stable Black Hole Horizons?