Existence of constant mean curvature foliation in the extended Schwarzschild spacetime

TL;DR

This paper constructs a family of constant mean curvature hypersurfaces in the Kruskal extension of Schwarzschild spacetime, extending previous work by Malec and d3 Murchadha, with mean curvature varying from minus to plus infinity.

Contribution

It introduces a new T-axisymmetric, spherically symmetric CMC foliation in the extended Schwarzschild spacetime with variable mean curvature.

Findings

Constructed a CMC foliation with mean curvature from -d8 to +d8.

Extended previous CMC foliation discussions to a broader class.

Demonstrated properties of the hypersurfaces in Kruskal extension.

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.