Time symmetric initial data for binary black holes in numerical relativity

Apr, 2003
27 pages
Published in:
  • Phys.Rev.D 68 (2003) 084002
e-Print:

Citations per year

200320082013201820232103
Abstract: (arXiv)
We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-Newtonian metric up to the 2PN order. It represents a non-linear deformation of the solution of Brill and Lindquist, i.e. an asymptotically flat region is connected to two asymptotically flat (in a certain weak sense) sheets, that are the images of the two singularities through appropriate inversion transformations. The total ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are computed by surface integrals performed at infinity. Using second order perturbation theory on the Brill-Lindquist background, we prove that the binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and in agreement with the known post-Newtonian result.
Note:
  • 27 pages, to appear in Phys. Rev. D
  • 04.30.-w
  • 97.60.Lf
  • 04.25.Dm
  • 97.60.Jd