Existence Of A Constant Mean Curvature Foliation In The Extended Schwarzschild Spacetime

We construct a T-axisymmetric, spacelike, spherically symmetric, constant mean curvature (CMC) hypersurface foliation in the Kruskal extension with properties such that the mean curvature varies in each slice and ranges from minus infinity to plus infinity. This family of hypersurfaces extends the CMC foliation discussions by Malec and O Murchadha in 2009 [Phys. Rev. D 80, 024017 (2009)].