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Excision boundary conditions for black-hole initial data

Gregory B. Cook*

Harald P. Pfeiffer†

  • Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, USA

  • Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125, USA

  • *Electronic address: cookgb@wfu.edu
  • †Electronic address: harald@tapir.caltech.edu
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Phys. Rev. D 70, 104016 – Published 12 November, 2004

DOI: https://doi.org/10.1103/PhysRevD.70.104016

Abstract

We define and extensively test a set of boundary conditions that can be applied at black-hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasicircular orbits and the determination of the innermost stable circular orbit. Our tests show that the boundary conditions work well.

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Outline

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Phys. Rev. D 70, 104016– Published 12 November, 2004
  • Received 23 July 2004

© 2004 American Physical Society

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