Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity
- Author(s)
- Michael Jasiulek, Mikolaj Korzynski
- Abstract
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(s)
- Gravitational Physics
- External organisation(s)
- Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut)
- Journal
- Classical and Quantum Gravity
- Volume
- 29
- No. of pages
- 14
- ISSN
- 0264-9381
- DOI
- https://doi.org/10.1088/0264-9381/29/15/155010
- Publication date
- 2012
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 1030 Physics, Astronomy
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/isometric-embeddings-of-2spheres-by-embedding-flow-for-applications-in-numerical-relativity(c0b96b41-a717-4ce3-b023-c308f871c54b).html