Simple Numerical Solutions to the Einstein Constraints on Various Three-Manifolds
arXiv:2208.01845 · doi:10.1007/s10714-022-03014-2
Abstract
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated non-constant mean curvature solution are computed on example manifolds from three of the eight Thursten geometrization classes. The constant mean curvature solutions found here are also solutions to the Yamabe problem that transforms a geometry into one with constant scalar curvature.
arXiv comment15 pages, 6 figures, published version
References in corpus (6)
- A multidomain spectral method for solving elliptic equations
- Initial Data for Numerical Relativity
- Improvements to the construction of binary black hole initial data
- Constructing Binary Neutron Star Initial Data with High Spins, High Compactness, and High Mass-Ratios
- Solving Partial Differential Equations Numerically on Manifolds with Arbitrary Spatial Topologies
- Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs