Study of the spacetime dynamics in Schwarzschild Geometry (SG) has always been in the lime light. Constant Mean Extrinsic Curvature (CMEC) hypersurfaces, also known as K-Surfaces, play an important role in SG. The talk spells out the importance of spacetime foliations and elaborates the behavior of K-surfaces for large values of K near essential singularity of Schwarzschild black hole.
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