IMEX evolution of scalar fields on curved backgrounds

Abstract

Inspiral of binary black holes occurs over a time-scale of many orbits, far longer than the dynamical time-scale of the individual black holes. Explicit evolutions of a binary system therefore require excessively many time steps to capture interesting dynamics. We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions, one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations. Our analysis considers the model problem of a forced scalar field propagating on a generic curved background. Nevertheless, we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity. Specializing to the Schwarzschild geometry in Kerr-Schild coordinates, we document the results of several numerical experiments testing our strategy.

28 pages, uses revtex4. Revised in response to referee's report. One numerical experiment added which incorporates perturbed initial data and adaptive time-stepping

References in corpus (6)

• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Solving Einstein's Equations With Dual Coordinate Frames
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Mergers of nonspinning black-hole binaries: Gravitational radiation characteristics
• Black-hole binary simulations: the mass ratio 10:1
• A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations

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• Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors
• Uncertainty in hybrid gravitational waveforms: Optimizing initial orbital frequencies for binary black-hole simulations
• Caustic echoes from a Schwarzschild black hole
• The Final Merger of Black-Hole Binaries
• Implicit-explicit (IMEX) evolution of single black holes
• A hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity
• Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity
• Numerical relativity simulations in the era of the Einstein Telescope