Pseudospectral implementation of the Einstein-Maxwell system

Abstract

Electromagnetism plays an important role in a variety of applications in gravity that we wish to investigate. To that end, in this work, we present an implementation of the Maxwell equations within the adaptive-mesh pseudospectral numerical relativity code BAMPS. We perform a thorough analysis of the evolution equations as a first order symmetric hyperbolic system of PDEs. This includes both the construction of the characteristic variables for use in our penalty boundary communication scheme, as well as radiation controlling, constraint preserving outer boundary conditions which, for the first time in a numerical context, are shown to be boundary-stable. After choosing a formulation of the Maxwell constraints that we may solve for initial data, we move on to show a suite of numerical tests. Our simulations, both within the Cowling approximation, and in full non-linear evolution, demonstrate rapid convergence of error with resolution, as well as consistency with known quasinormal decay rates on the Kerr background. Finally we evolve the electrovacuum equations of motion with strong data, a good representation of typical critical collapse runs.

29 pages, 10 figures. Matches the published version

References in corpus (40)

• Quasinormal modes of black holes and black branes
• Evolution of Binary Black Hole Spacetimes
• On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
• Numerical Relativity Using a Generalized Harmonic Decomposition
• A New Generalized Harmonic Evolution System
• Constraint damping in the Z4 formulation and harmonic gauge
• Critical phenomena in gravitational collapse
• Spectral Methods for Numerical Relativity
• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• Multi-dimensional Numerical Scheme for Resistive Relativistic MHD
• Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
• Binary black holes' effects on electromagnetic fields
• Key Elements of Robustness in Binary Black Hole Evolutions using Spectral Methods
• Problems which are well-posed in a generalized sense with applications to the Einstein equations
• An Introduction to Well-posedness and Free-evolution
• Collisions of charged black holes
• A Pseudospectral Method for Gravitational Wave Collapse
• Implementation of higher-order absorbing boundary conditions for the Einstein equations
• A 3+1 covariant suite of Numerical Relativity Evolution Systems
• The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes
• Towards absorbing outer boundaries in General Relativity
• Collisions of oppositely charged black holes
• Testing the nonlinear stability of Kerr-Newman black holes
• Strongly hyperbolic systems in General Relativity
• Outer boundary conditions for Einstein's field equations in harmonic coordinates
• Critical phenomena in the gravitational collapse of electromagnetic waves
• Hyperbolic Relaxation Method for Elliptic Equations
• Absorbing boundary conditions for Einstein's field equations
• Evolution of Brill waves with an adaptive pseudospectral method
• Adaptive hp-Refinement for Spectral Elements in Numerical Relativity
• Hyperbolicity of Physical Theories with Application to General Relativity
• Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves
• Does charge matter in high-energy collisions of black holes?
• Twist-free axisymmetric critical collapse of a complex scalar field
• Formulation Improvements for Critical Collapse Simulations
• The initial boundary value problem for free-evolution formulations of General Relativity
• General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method
• Can quasi-circular mergers of charged black holes produce extremal black holes?
• Extremal black hole formation as a critical phenomenon
• Universality in the Critical Collapse of the Einstein-Maxwell System