Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints

Abstract

In this paper, we continue our investigations of Rácz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which we were able to resolve by introducing a certain modification of Rácz's parabolic-hyperbolic formulation. The primary focus of the present paper here is the asymptotically hyperboloidal setting. We provide evidence through a mixture of numerical and analytical methods that the asymptotics of the solutions of Rácz's parabolic-hyperbolic formulation is stable, and, in particular, no modifications are necessary to obtain solutions that are asymptotically hyperboloidal.

Only minor changes. Matches the published version

References in corpus (5)

• The Constraint Equations
• Cauchy problem as a two-surface based `geometrodynamics'
• A spectral solver for evolution problems with spatial S3-topology
• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• Is the Bianchi identity always hyperbolic?

Cited by in corpus (2)

• Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?
• Hyperboloidal initial data without logarithmic singularities