Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum

Abstract

We analytically construct initial data for binary black hole systems by solving the Einstein constraint equations within the Bowen-York framework. Allowing for arbitrarily oriented linear momenta and spins, we obtain a perturbative solution of the vacuum Hamiltonian constraint up to third order in the source parameters. Our solution explicitly incorporates the system's binary nature via position-weighted multipole moments. The momentum constraints are solved exactly, while the conformal factor is determined analytically. Using the resulting initial data, we compute the ADM energy, linear and angular momenta, and the irreducible mass. We also determine the shape of the apparent horizon and show that it is geometrically consistent with the inner-end regularity. The resulting expressions are written in a manifestly tensorial form and provide an analytic benchmark for numerical-relativity calculations within the perturbative far-zone regime considered here.

19 pages, title has changed, v2 is significantly improved and matches the published version

References in corpus (18)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• The Dynamics of General Relativity
• Evolution of Binary Black Hole Spacetimes
• The North American Nanohertz Observatory for Gravitational Waves
• A single-domain spectral method for black hole puncture data
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• Black-hole binaries, gravitational waves, and numerical relativity
• Extrinsic Curvature and the Einstein Constraints
• Numerical Relativity and Compact Binaries
• GW231123: a Binary Black Hole Merger with Total Mass 190-265 $M_{\odot }$
• Nonexistence of conformally flat slices of the Kerr spacetime
• Evolving the Bowen-York initial data for spinning black holes
• Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
• Approximate initial data for binary black holes
• Non-stationary Energy in General Relativity
• Approximate analytical description of apparent horizons for initial data with momentum and spin
• Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism