Physics and Initial Data for Multiple Black Hole Spacetimes

Abstract

An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital parameters, including the frequency and separation at the inner-most stable circular orbit (ISCO). One approach to estimating these parameters relies on a sequence of initial data slices that attempt to capture the physics of the inspiral. Using calculations of the binding energy, several authors have estimated the ISCO parameters using initial data constructed with various algorithms. In this paper we examine this problem using conformally Kerr-Schild initial data. We present convergence results for our initial data solutions, and give data from numerical solutions of the constraint equations representing a range of physical configurations. In a first attempt to understand the physical content of the initial data, we find that the Newtonian binding energy is contained in the superposed Kerr-Schild background before the constraints are solved. We examine some deficiencies with the initial data approach to orbiting binaries, especially touching on the effects of prior motion and spin-orbital coupling of the angular momenta. Making rough estimates of these effects, we find that they are not insignificant compared to the binding energy, leaving some doubt of the utility of using initial data to predict ISCO parameters. In computations of specific initial-data configurations we find spin-specific effects that are consistent with analytical estimates.

41 pages, 17 figures

References in corpus (12)

• Introduction to Isolated Horizons in Numerical Relativity
• A multidomain spectral method for solving elliptic equations
• Binary black holes in circular orbits. II. Numerical methods and first results
• Binary black holes in circular orbits. I. A global spacetime approach
• Corotating and irrotational binary black holes in quasi-circular orbits
• Comparing initial-data sets for binary black holes
• Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?
• Tidal interaction in binary black hole inspiral
• Tracking Black Holes in Numerical Relativity
• Black Hole Interaction Energy
• Last orbits of binary black holes
• Local and global properties of conformally flat initial data for black hole collisions

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• Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions
• Beyond the Bowen-York extrinsic curvature for spinning black holes
• Circumbinary Disk Accretion into Spinning Black Hole Binaries
• The initial value problem as it relates to numerical relativity
• Puncture Initial Data for Black-Hole Binaries with High Spins and High Boosts
• Quasi-equilibrium Binary Black Hole Initial Data for Dynamical Evolutions
• Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity
• Generic initial data for binary boson stars
• Radiation Memory, Boosted Schwarzschild Spacetimes and Supertranslations
• Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries
• Time-symmetric initial data for binary black holes in numerical relativity
• Kerr Black Holes and Nonlinear Radiation Memory
• Boosted Schwarzschild Metrics from a Kerr-Schild Perspective
• Junction Conditions and local Spacetimes in General Relativity
• Toward computing gravitational initial data without elliptic solvers
• Tips for implementing multigrid methods on domains containing holes
• Black hole initial data from a non-conformal decomposition
• A simple method of constructing binary black hole initial data
• Evolution of circumbinary accretion disk around supermassive binary black hole: post-Newtonian hydrodynamics versus Newtonian hydrodynamics
• Hyperbolicity and Constrained Evolution in Linearized Gravity
• Area Invariance of Apparent Horizons under Arbitrary Boosts
• Momentum constraint relaxation