Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
arXiv:2002.06759 · doi:10.1103/PhysRevD.101.084013
Abstract
In this paper we continue earlier investigations of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by Rácz. Motivated by the strong evidence from these works that the resulting vacuum initial data sets are generically not asymptotically flat we analyse the asymptotics of the solutions of a modified formulation by a combination of analytical and numerical techniques. We conclude that the vacuum initial data sets generated with this new formulation are generically asymptotically flat.
arXiv comment30 pages. 8 figures. Matches the published version
References in corpus (25)
- Einstein Constraints on Asymptotically Euclidean Manifolds
- Initial Data and Coordinates for Multiple Black Hole Systems
- Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
- Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
- Black Hole Data via a Kerr-Schild Approach
- Constraints as evolutionary systems
- Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics
- Cauchy problem as a two-surface based `geometrodynamics'
- A spectral solver for evolution problems with spatial S3-topology
- Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
- Including realistic tidal deformations in binary black-hole initial data
- A spectral method for half-integer spin fields based on spin-weighted spherical harmonics
- Numerical Bifurcation Analysis of the Conformal Method
- On the center of mass of asymptotically hyperbolic initial data sets
- Kerr-Schild type initial data for black holes with angular momenta
- Is the Bianchi identity always hyperbolic?
- Toward computing gravitational initial data without elliptic solvers
- Asymptotics of solutions of a hyperbolic formulation of the constraint equations
- Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
- Construction of high precision numerical single and binary black hole initial data
- On the evolutionary form of the constraints in electrodynamics
- Black hole initial data from a non-conformal decomposition
- The Algebraic-Hyperbolic Approach to the Linearized Gravitational Constraints on a Minkowski Background
- Criticality of inhomogeneous Nariai-like cosmological models
- Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints