Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints
arXiv:2104.10290 · doi:10.1088/1361-6382/ac79f1
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.
arXiv commentOnly minor changes. Matches the published version
References in corpus (20)
- Initial Data and Coordinates for Multiple Black Hole Systems
- Black Hole Data via a Kerr-Schild Approach
- Constraints as evolutionary systems
- Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
- Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics
- The Constraint Equations
- Cauchy problem as a two-surface based `geometrodynamics'
- Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
- A spectral solver for evolution problems with spatial S3-topology
- A spectral method for half-integer spin fields based on spin-weighted spherical harmonics
- Numerical investigations of the asymptotics of solutions to the evolutionary form of the constraints
- On the center of mass of asymptotically hyperbolic initial data sets
- Numerical Bifurcation Analysis of the Conformal Method
- Is the Bianchi identity always hyperbolic?
- Kerr-Schild type initial data for black holes with angular momenta
- 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
- Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
- Black hole initial data from a non-conformal decomposition
- Criticality of inhomogeneous Nariai-like cosmological models