Adaptive computation of gravitational waves from black hole interactions

Abstract

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$ modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes.

16 Pages, RevTeX, 13 figures

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Cited by in corpus (14)

• Evolutions in 3D numerical relativity using fixed mesh refinement
• Numerical Relativity: A review
• Evolving a puncture black hole with fixed mesh refinement
• Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
• Multigrid elliptic equation solver with adaptive mesh refinement
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• Interface Conditions for Wave Propagation Through Mesh Refinement Boundaries
• Adaptive mesh refinement approach to construction of initial data for black hole collisions
• Numerical Relativity and Inhomogeneous Cosmologies
• Non-linear harmonic generation in finite amplitude black hole oscillations
• Three-dimensional adaptive evolution of gravitational waves in numerical relativity
• The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
• Classical back reaction of low-frequency cosmic gravitational radiation