Hypersurfaces and junction conditions are supported in GRTensorIII 2.0 for Maple.
Hypersurfaces can be defined and the extrinsic curvature and constraint equations can be evaluated. Support is provided for timelike, spacelike and null hypersurfaces in a four dimensional spacetime.
Junctions of two spacetime manifolds by the identification of a common hypersurface can be performed and the Darmois-Israel junction conditions can be calculated (for null hypersurfaces, the Barrabes-Israel conditions). The stress-energy of any resulting shell and equations for shell evolution can be determined.
A number of example worksheets are provided. In most cases they follow the examples provided in “A Relativist’s Toolkit” by Eric Poisson.
This update brings the features formerly found in the GRJunction package directly into GRTensorIII.
GRTensorIII is available on github at: https://github.com/grtensor/grtensor
GRTensorIII requires Maple (http://www.maplesoft.com/)
The hypersurface and junction documentation can be viewed at: