Erratum: Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits [Phys. Rev. D70, 044044 (2004)]

Abstract

Two relations, the virial relation MADM = MK and the first law in the form δMADM = ΩδJ, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, MADM, MK, J, and Ω are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. δ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between MADM and MK and between δMADM and ΩδJ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

Numerical method for binary black hole/neutron star initial data: Code test

“…Our new numerical method is applicable for various formulations including spatially confomal flat initial data [22], the Isenberg-Wilson-Mathews (IWM) formulation [23,24,25], and waveless approximation [26]. We introduce the IWM formulation used for a test calculation of our new code.…”

“…We compute the solution (26) numerically by imposing boundary conditions at the sphere r a = M/2. In order to test the code using Dirichlet boundary conditions, we set the boundary value at r = r a to the exact value computed from (26). For testing Neumann boundary condition, we take the value of the derivative of (26).…”

Approximate initial data for binary black holes

“…[7][8][9][10]; see also [11][12][13][14] for alternative ways of constructing binary black hole initial data.) There is general consensus that the latter formalism is better suited for the construction of quasiequilibrium data (but see [15] for a very promising alternative approach), even though, at least in terms of global quantities, both formalisms lead to very similar results for configurations outside the innermost stable circular orbit (see, e.g., [9,16]). …”

Circular orbits and spin in black-hole initial data

“…[46]). However a more selfconsistent approach has been developed by Shibata et al [47,48] for the case of neutron-star binaries and it should be possible to adapt this approach to black-hole binaries in the future.…”