A New Method for Solving the Initial Value Problem with Application to Multiple Black Holes

Abstract

This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified components of the extrinsic curvature we solve for extrinsic curvature's remaining components. For the second part, after noting that initial data for the Kerr spacetime can be derived within our formalism we construct data for axisymmetric configurations of spinning black holes. Though our method is limited to axisymmetry, it offers an advantage over the Bowen-York proceedure that our data approach those for Kerr holes in the limit of large separations and in the close limit.

10 pages

References in corpus (3)

• Boosted three-dimensional black-hole evolutions with singularity excision
• Gravitational wave extraction and outer boundary conditions by perturbative matching
• Evolving the Bowen-York initial data for spinning black holes

Cited by in corpus (10)

• Second order gauge invariant gravitational perturbations of a Kerr black hole
• New conformally flat initial data for spinning black holes
• Initial data for two Kerr-like black holes
• Initial data for a head on collision of two Kerr-like black holes with close limit
• Adaptive mesh refinement approach to construction of initial data for black hole collisions
• Potentials for transverse trace-free tensors
• New solutions of initial conditions in general relativity
• Coordinate independent expression for transverse trace-free tensors
• Decoupling the momentum constraints in general relativity
• Asymptotically flat and regular Cauchy data