Conformal Thin-Sandwich Solver for Generic Initial Data

TL;DR

This paper introduces a flexible conformal thin-sandwich method for generating initial data in Einstein's equations, capable of handling complex scenarios like black hole mergers without simplifying assumptions.

Contribution

It develops a new scheme that avoids conformal flatness and Killing vector assumptions, including superposition-based free data and singularity handling without excision.

Findings

Successfully generated initial data for binary black hole mergers

Demonstrated the method's applicability to black hole-neutron star systems

Validated the approach with ultrarelativistic collision simulations

Abstract

We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for determining free data based on superposition, as well as a way to handle black hole singularities without excision. We numerically solve the constraint equations using a multigrid algorithm with mesh refinement. We demonstrate the efficacy of the method with initial data solutions for several applications: a quasicircular binary black hole merger, a dynamical capture black hole-neutron star merger, and an ultrarelativistic collision.