Existence of constant mean curvature foliation in the extended Schwarzschild spacetime

Abstract

We construct a $T$-axisymmetric, spacelike, spherically symmetric, constant mean curvature hypersurfaces foliation in the Kruskal extension with properties 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 posted by Malec and \'{O} Murchadha in 2009.