A Galerkin-Collocation domain decomposition method: application to the evolution of cylindrical gravitational waves

Abstract

We present a Galerkin-Collocation domain decomposition algorithm applied to the evolution of cylindrical unpolarized gravitational waves. We show the effectiveness of the algorithm in reproducing initial data with high localized gradients and in providing highly accurate dynamics. We characterize the gravitational radiation with the standard Newman-Penrose Weyl scalar ${\Psi }_4$. We generate wave templates for both polarization modes, $\times$ and $+$, outgoing and ingoing, to show how they exchange energy nonlinearly. In particular, considering an initially ingoing $\times$ wave, we were able to trace a possible imprint of the gravitational analog of the Faraday effect in the generated templates.

20 pages, 8 figures. Accepted in Class. Quantum Grav

References in corpus (4)

• The SXS Collaboration catalog of binary black hole simulations
• Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes
• Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity
• Nonlinear evolution of cylindrical gravitational waves: numerical method and physical aspects

Cited by in corpus (3)

• The Bondi problem revisited: a spectral domain decomposition code
• Multidomain Galerkin-Collocation method: characteristic spherical collapse of scalar fields
• Multidomain Galerkin-Collocation method: spherical collapse of scalar fields II