1993
DOI: 10.1103/physrevd.47.1471
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Abstract: We describe three numerical approaches to the construction of three-dimensional initial data for the collision of two black holes. The first of our approaches involves finite differencing the 3 + 1 Hamiltonian constraint equation on a Cadei coordinate grid. The difference equations are then solved via the multigrid algorithm. The second approach also uses finite-difference techniques, but this time on a regular Cartesian coordinate grid. A Cartesian grid has the advantage of having no coordinate singularities.… Show more

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Cited by 58 publications
(97 citation statements)
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“…Also, we assume that there in no matter on S, so R µν = 0. While conditions (17), (18) and (20) are coordinate independent, our next and final demand breaks precisely this coordinate freedom: We demand that the coordinate location of the apparent horizon does not move initially in an evolution of the initial data.…”
Section: Black-hole Excision Boundary Conditionsmentioning
confidence: 99%
See 2 more Smart Citations
“…Also, we assume that there in no matter on S, so R µν = 0. While conditions (17), (18) and (20) are coordinate independent, our next and final demand breaks precisely this coordinate freedom: We demand that the coordinate location of the apparent horizon does not move initially in an evolution of the initial data.…”
Section: Black-hole Excision Boundary Conditionsmentioning
confidence: 99%
“…Boundary conditions based on this idea have been used successfully for generating general black-hole initial data using various initial-data decompositions [14,15,16,17]. Their first use in conjunction with the conformal thinsandwich decomposition [9,18] was only partially successful due to an unavoidable constraint violation.…”
Section: Black-hole Excision Boundary Conditionsmentioning
confidence: 99%
See 1 more Smart Citation
“…In this paper, we will follow Cook et.al. [10,16,17] and choose a flat background geometry, but we will choose a three-sheeted topology as opposed to the twosheeted topology of Cook.…”
Section: A the Initial Value Problemmentioning
confidence: 99%
“…For us, it is inherently 3-dimensional since we want to be able to specify arbitrary boost and spin directions for each hole. The methods in most frequent use [3,4] are based on an approach which chooses maximal spatial hypersurfaces (K = 0) and takes the spatial 3-metric to be conformally flat (g ij = φ 4 δ ij , φ being the conformal factor). Under these conditions, the Hamiltonian constraint can be decoupled from the momentum constraint.…”
Section: Introduction and Methodsmentioning
confidence: 99%