Toward computing gravitational initial data without elliptic solvers

Abstract

Two new methods have been proposed for solving the gravitational constraints without using elliptic solvers by formulating them as either an algebraic-hyperbolic or parabolic-hyperbolic system. Here, we compare these two methods and present a unified computational infrastructure for their implementation as numerical evolution codes. An important potential application of these methods is the prescription of initial data for the simulation of black holes. This paper is meant to support progress and activity in that direction.

Title and presentation changed

References in corpus (5)

• Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
• Constraints as evolutionary systems
• Cauchy problem as a two-surface based `geometrodynamics'
• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• The Algebraic-Hyperbolic Approach to the Linearized Gravitational Constraints on a Minkowski Background

Cited by in corpus (6)

• Elliptica: a new pseudo-spectral code for the construction of initial data
• Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
• Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?
• Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints
• Hyperboloidal initial data without logarithmic singularities