2000/01/31 by Pedro Marronetti, P. Marronetti, M. Huq +9 · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.62.024017
published as Phys.Rev. D62 (2000) 024017 · 6 pages, 5 postscript figures. Minor changes and some points clarified. Accepted for publication in Phys. Rev. D
arxiv created 2000/04/10 · openalex publication_date 2000/06/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with l1 and l_\ensuremath∞ norms of violation of the constraint equations falling below those of the truncation error (residual error due to discretization) present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of h=M/4, and an ``attenuated'' superposition yields data usable to resolutions at least as fine as h=M/8. In addition, the attenuated approximate data may be more tractable in a full (computational) exact solution to the initial value problem.