Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits

摘要

Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first lawin the form $\delta M_{\rm ADM}=\Omega \delta J$, should be satisfied by asolution and a sequence of solutions describing binary compact objects inquasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and$\Omega$ are the ADM mass, Komar mass, angular momentum, and orbital angularvelocity, respectively. $\delta$ denotes an Eulerian variation. These twoconditions restrict the allowed formulations that we may adopt. First, wederive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $\deltaM_{\rm ADM}$ and $\Omega \delta J$ for general asymptotically flat spacetimes.Then, to obtain solutions that satisfy the virial relation and sequences ofsolutions that satisfy the first law at least approximately, we propose aformulation for computation of quasiequilibrium binary neutron stars in generalrelativity. In contrast to previous approaches in which a part of the Einsteinequation is solved, in the new formulation, the full Einstein equation issolved with maximal slicing and in a transverse gauge for the conformalthree-metric. Helical symmetry is imposed in the near zone, while in thedistant zone, a waveless condition is assumed. We expect the solutions obtainedin this formulation to be excellent quasiequilibria as well as initial data fornumerical simulations of binary neutron star mergers.