Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
arXiv:1301.6174 · doi:10.1088/0264-9381/27/3/035014
Abstract
We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with tracefree energy-momentum tensor. Two examples are studied in detail, a conformally coupled scalar field and a Yang-Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang-Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang-Mills fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang-Mills is found to exhibit some nontrivial gauge dynamics.
28 pages, 9 figures. Minor changes to agree with journal version
References in corpus (14)
- Hyperboloidal evolution with the Einstein equations
- Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
- Regularity of the Einstein Equations at Future Null Infinity
- Implementation of higher-order absorbing boundary conditions for the Einstein equations
- Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
- Improved outer boundary conditions for Einstein's field equations
- Towards absorbing outer boundaries in General Relativity
- Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
- Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
- Black hole initial data on hyperboloidal slices
- Regularization of spherical and axisymmetric evolution codes in numerical relativity
- Absorbing boundary conditions for Einstein's field equations
- Numerical Relativity and Asymptotic Flatness
- A note on boundary value problems for black hole evolutions
Cited by in corpus (41)
- The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model
- Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
- An Introduction to Well-posedness and Free-evolution
- Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordström case
- Hyperboloidal framework for the Kerr spacetime
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution
- Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
- Axisymmetric fully spectral code for hyperbolic equations
- Black hole initial data on hyperboloidal slices
- Superradiance of a charged scalar field coupled to the Einstein-Maxwell equations
- Scalar Field Dark Matter: behavior around black holes
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution II: gauge conditions
- The affine-null metric formulation of Einstein's equations
- The Hyperboloidal Numerical Evolution of a Good-Bad-Ugly Wave Equation
- Initial data for perturbed Kerr black holes on hyperboloidal slices
- Global simulations of Minkowski space-time including space-like infinity
- Formation and decay of Einstein-Yang-Mills black holes
- Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c
- Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
- Evolution of a mass-less test scalar field on Boson Stars space-times
- Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space
- Spherically symmetric black hole spacetimes on hyperboloidal slices
- Summation by Parts and Truncation Error Matching on Hyperboloidal Slices
- Boundary Conditions for the Gravitational Field
- Free evolution of the hyperboloidal initial value problem in spherical symmetry
- Axisymmetric constant mean curvature slices in the Kerr space-time
- Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
- Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions
- The initial boundary value problem for free-evolution formulations of General Relativity
- Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
- Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method
- The shear-free condition and constant-mean-curvature hyperboloidal initial data
- Avenues for Analytic exploration in Axisymmetric Spacetimes. Foundations and the Triad Formalism
- Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity
- Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
- Conformal compactification and affine-null metric formulation of the Einstein equations
- A numerical approach to particle creation in accelerating toy models
- Nonlinear Evolution of unstable Charged de Sitter Black Holes with Hyperboloidal Formalism
- Numerical and analytical methods for asymptotically flat spacetimes
- The non-linear perturbation of a black hole by gravitational waves. I. The Bondi-Sachs mass loss
- Hyperboloidal neutron star and black hole initial data in spherical symmetry