FOLIATION AND ISOMETRIC EMBEDDINGS ψ (2 S OF SCHWARZSCHILD SPACETIME

Abstract

Last decades have witnessed remarkable progress in using numerical tools in solving Einstein Field Equations. For qualitative and quantitative analysis of black hole spacetime, the tools of ’Foliation of Spacetime’, ’Effective Potential for the geodesics of particles’ and ’Isometric Embeddings’ are discussed in an elaborative manner with particular reference to the work of Brill et al. Using compactified Kruskal-Szekeres coordinate transformations, complete foliation has been performed with Constant Mean Extrinsic Hypersurfaces (K-Surfaces) and Free Falling Hypersurfaces (ψN - Hypersurfaces). K-Surfaces and ψN -Hypersurfaces which smoothly pass through r = 2m, are helpful for the procedure of canonical quantization of massive scalar fields. Isometric Embeddings for a variety of K-Surfaces and Effective Potentials for the geodesic of massless and massive particles by using all values of K, are numerically calculated and displayed graphically. These tools and methodology would be helpful in research on the geometries of many other curved spacetimes.