Numerical construction of initial data for Einstein's equations with static extension to space-like infinity

Abstract

We describe a numerical method to construct Cauchy data extending to space-like infinity based on Corvino's (2000) gluing method. Adopting the setting of Giulini and Holzegel (2005), we restrict ourselves here to vacuum axisymmetric spacetimes and glue a Schwarzschildean end to Brill-Lindquist data describing two non-rotating black holes. Our numerical implementation is based on pseudo-spectral methods, and we carry out extensive convergence tests to check the validity of our numerical results. We also investigate the dependence of the total ADM mass on the details of the gluing construction.

20 pages, 13 figures. Agrees with the published version

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Cited by in corpus (4)

• Global simulations of Minkowski space-time including space-like infinity
• Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
• Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild
• Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data