# Illustrating stability properties of numerical relativity in electrodynamics

@article{Knapp2002IllustratingSP, title={Illustrating stability properties of numerical relativity in electrodynamics}, author={A. M. Knapp and Eve J. Walker and Thomas W. Baumgarte}, journal={Physical Review D}, year={2002}, volume={65}, pages={064031} }

We show that a reformulation of the Arnowitt-Deser-Misner 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…

## 20 Citations

### Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

- Physics
- 2014

A bstractA variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of…

### Numerical stability for finite difference approximations of Einstein's equations

- MathematicsJ. Comput. Phys.
- 2006

### Improved numerical stability of stationary black hole evolution calculations

- Physics
- 2002

We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical…

### General Relativistic Magnetohydrodynamics for the Numerical Construction of Dynamical Spacetimes

- Physics, Mathematics
- 2002

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3 + 1 form. These consist of the complete coupled set of Maxwell's equations for the electromagnetic field, Einstein's…

### Energy norms and the stability of the Einstein evolution equations

- Mathematics
- 2002

The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for…

### Dynamical formation of Proca stars and quasistationary solitonic objects

- PhysicsPhysical Review D
- 2018

We perform fully non-linear numerical simulations within the spherically symmetric Einstein-(complex)Proca system. Starting with Proca field distributions that obey the Hamiltonian, momentum and…

### A remedy for constraint growth in numerical relativity: the Maxwell case

- Physics
- 2004

Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem, we investigate the effect of adding spatial derivatives of the constraints…

### Hyperbolic formulations of general relativity with Hamiltonian structure

- Physics
- 2012

With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of…

### Numerical studies of constraints and gravitational wave extraction in general relativity

- Physics
- 2004

Title of Dissertation: Numerical studies of constraints and gravitational wave extraction in general relativity David Robert Fiske, Doctor of Philosophy, 2004 Dissertation directed by: Professor…

### A model problem for the initial-boundary value formulation of Einstein's field equations

- Mathematics
- 2004

In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such…

## References

SHOWING 1-4 OF 4 REFERENCES

### Living Rev

- Rel. 1, 3
- 1998

### Phys

- Rev. D 61, 087501
- 2000

### La gravifique einsteinienne (Gauthier- Villars

- Paris, 1921); C. Lanczos, Phys. Z. 23, 537
- 1922