Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

Autor(en)

Michael Jasiulek, Mikolaj Korzynski

Abstrakt

We present a numerical method for solving Weyl's embedding problem which consists in finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean 3-space. The method is based on a construction introduced by Weingarten and was used in Nirenberg's proof of Weyl's conjecture. The target embedding results as the endpoint of an embedding flow in R-3 beginning at the unit sphere's embedding. We employ spectral methods to handle functions on the surface and to solve various ( non) linear elliptic PDEs. The code requires no additional input or steering from the operator and its convergence is guaranteed by the Nirenberg arguments. Possible applications in 3 + 1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut)

Journal

Classical and Quantum Gravity

Band

29

Anzahl der Seiten

14

ISSN

0264-9381

DOI

https://doi.org/10.1088/0264-9381/29/15/155010

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

1030 Physik, Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/c0b96b41-a717-4ce3-b023-c308f871c54b