Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild
arXiv:1902.05670 · doi:10.1088/1361-6382/ab34d8
Abstract
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our (pseudo)-spectral scheme is demonstrated under the assumption of axisymmetry so as to fashion composite Hamiltonian constraint satisfying initial data featuring internal binary black holes (BBH) as glued to exterior Schwarzschild initial data in isotropic form. The generality of the method is illustrated in a comparison of the ADM mass of EAG initial data sets featuring internal BBHs as modelled by Brill-Lindquist and Misner data.In contrast to the recent work of Doulis and Rinne (2016), and Pook-Kolb and Giulini (2018) we do not make use of the York-Lichnerowicz conformal framework to reformulate the constraints.
References in corpus (18)
- Initial Data for Numerical Relativity
- Spectral Methods for Numerical Relativity
- Existence of non-trivial, vacuum, asymptotically simple space-times
- Initial data engineering
- The eth formalism in numerical relativity
- On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
- Gluing and wormholes for the Einstein constraint equations
- Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
- On the topology of vacuum spacetimes
- Construction of N-body initial data sets in general relativity
- Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
- Construction of initial data for 3+1 numerical relativity
- Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes
- Gluing Initial Data Sets for General Relativity
- The initial value problem as it relates to numerical relativity
- A spectral method for half-integer spin fields based on spin-weighted spherical harmonics
- Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
- Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data