The initial value problem in numerical relativity

TL;DR

This paper reviews methods for constructing initial data in numerical relativity, focusing on the conformal approach, recent numerical techniques, and innovative strategies for realistic binary black hole simulations.

Contribution

It compares Hamiltonian and Lagrangian formalisms, introduces a weight-function in extrinsic curvature decomposition, and discusses new numerical methods for astrophysical initial data.

Findings

Advantages of the weight-function in extrinsic curvature decomposition

Progress in numerical techniques for elliptic equations

Innovative approaches for realistic binary black hole initial data

Abstract

The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical techniques to solve the resulting elliptic equations, and explore innovative approaches toward the construction of astrophysically realistic initial data for binary black hole simulations.