Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data

Pook-Kolb, Daniel; Giulini, Domenico

doi:10.1088/1361-6382/aaff0f

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Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data

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Pook-Kolb, Daniel
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Citation

Pook-Kolb, D., & Giulini, D. (2019). Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data. Classical and Quantum Gravity, 36(4): 045011. doi:10.1088/1361-6382/aaff0f.

Cite as: https://hdl.handle.net/21.11116/0000-0002-5745-F

Abstract

Building on the work of Giulini and Holzegel (2005), a new numerical approach
is developed for computing Cauchy data for Einstein's equations by gluing a
Schwarzschild end to a Brill-Lindquist metric via a Corvino-type construction.
In contrast to, and in extension of, the numerical strategy of Doulis and Rinne
(2016), the overdetermined Poisson problem resulting from the Brill wave ansatz
is decomposed to obtain two uniquely solvable problems. A pseudospectral method
and Newton-Krylov root finder are utilized to perform the gluing. The
convergence analysis strongly indicates that the numerical strategy developed
here is able to produce highly accurate results. It is observed that
Schwarzschild ends of various ADM masses can be glued to the same interior
configuration using the same gluing radius.