A new numerical scheme to compute 3D configurations of quasiequilibrium compact stars in general relativity -- Application to synchronously rotating binary star systems --

TL;DR

This paper introduces a novel numerical method for calculating the 3D quasiequilibrium configurations of compact stars, especially binary neutron stars, in general relativity, avoiding the conformal flatness approximation.

Contribution

The authors develop a new numerical scheme that directly solves Einstein's equations for 3D nonaxisymmetric configurations without assuming conformal flatness.

Findings

Successfully computed equilibrium sequences of binary polytropic stars in general relativity.

Validated the scheme with Newtonian and axisymmetric relativistic star models.

Extended the method to nonaxisymmetric binary systems with various polytropic indices.

Abstract

We have developed a new numerical scheme to obtain quasiequilibrium structures of nonaxisymmetric compact stars such as binary neutron star systems as well as the spacetime around those systems in general relativity. Concerning quasiequilibrium states of binary systems in general relativity, several investigations have been already carried out by assuming conformal flatness of the spatial part of the metric. However, the validity of the conformally flat treatment has not been fully analyzed except for axisymmetric configurations. Therefore it is desirable to solve quasiequilibrium states by developing totally different methods from the conformally flat scheme. In this paper we present a new numerical scheme to solve directly the Einstein equations for 3D configurations without assuming conformal flatness, although we make use of the simplified metric for the spacetime. This new formulation is the extension of the scheme which has been successfully applied for structures of axisymmetric rotating compact stars in general relativity. It is based on the integral representation of the Einstein equations by taking the boundary conditions at infinity into account. We have checked our numerical scheme by computing equilibrium sequences of binary polytropic star systems in Newtonian gravity and those of axisymmetric polytropic stars in general relativity. We have applied this numerical code to binary star systems in general relativity and have succeeded in obtaining several equilibrium sequences of synchronously rotating binary polytropes with the polytropic indices N = 0.0, 0.5 and 1.0.