Constraint-satisfying binary boson star initial data via XCFC

TL;DR

This paper introduces a new method using the XCFC formalism to generate initial data for scalar-field systems in numerical relativity, ensuring constraint satisfaction and improving upon superposition techniques.

Contribution

The authors develop an iterative XCFC-based approach to produce constraint-satisfying initial data for scalar fields, including boson star binaries, overcoming previous convergence issues.

Findings

The XCFC method converges for various scalar-field configurations.

It produces genuinely constraint-satisfying initial data for boson star binaries.

It outperforms superposition approaches in accuracy and constraint satisfaction.

Abstract

Numerical-relativity simulations with non-trivial matter configurations require initial data that satisfy the Hamiltonian and momentum constraints of the Einstein equations. We construct constraint-satisfying scalar-field initial data using the eXtended Conformally Flat Condition (XCFC) formalism, in which the matter variables are conformally rescaled and an auxiliary vector field is introduced. In doing so, we overcome the issues of local uniqueness and convergence of the solutions that arise in the second-order elliptic equations associated with the constraints. Using an iterative solver method, we demonstrate the convergence of the XCFC approach to a solution for several scalar-field matter systems. Those include Gaussian-like profiles, topological torus configurations, and equal-mass boson star binaries. In particular, for the latter case, it is common to employ the superposition of two isolated boson star solutions in order to build the initial data. We show that our formalism significantly improves upon a superposition approach by generating genuinely constraint-satisfying initial data for boson star binaries.