The Algebraic-Hyperbolic Approach to the Linearized Gravitational Constraints on a Minkowski Background

Abstract

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein's equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

Clarification added

References in corpus (2)

• Construction of initial data for 3+1 numerical relativity
• Constraints as evolutionary systems

Cited by in corpus (4)

• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
• Toward computing gravitational initial data without elliptic solvers
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations