Illustrating Stability Properties of Numerical Relativity in Electrodynamics

Abstract

We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate both the original and the revised versions of Maxwell's equations, and show that their distinct numerical behavior reflects the properties found in linearized general relativity. Our results shed further light on the stability properties of general relativity, illustrate them in a very transparent context, and may provide a useful framework for further improvement of numerical schemes.

5 pages, 2 figures, to be published as Brief Report in Physical Review D

References in corpus (2)

• A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
• Constraint propagation in the family of ADM systems

Cited by in corpus (21)

• Numerical Relativity and Compact Binaries
• Constraining axion inflation with gravitational waves from preheating
• Improved numerical stability of stationary black hole evolution calculations
• General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes
• An Introduction to Well-posedness and Free-evolution
• Dynamical formation of Proca stars and quasi-stationary solitonic objects
• Hyperbolicity of second-order in space systems of evolution equations
• The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes
• Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints
• Numerical stability of the Z4c formulation of general relativity
• Numerical stability for finite difference approximations of Einstein's equations
• New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields
• Energy Norms and the Stability of the Einstein Evolution Equations
• A model problem for the initial-boundary value formulation of Einstein's field equations
• Excising das All: Evolving Maxwell waves beyond scri
• NRPyElliptic: A Fast Hyperbolic Relaxation Elliptic Solver for Numerical Relativity, I: Conformally Flat, Binary Puncture Initial Data
• A remedy for constraint growth in Numerical Relativity
• Toward Making the Constraint Hypersurface an Attractor in Free Evolution
• Numerical stability of the AA evolution system compared to the ADM and BSSN systems
• Hyperbolic formulations of General Relativity with Hamiltonian structure
• Pseudospectral implementation of the Einstein-Maxwell system