Constant mean curvature slicings of Kantowski-Sachs spacetimes
J. Mark Heinzle
TL;DR
This paper studies the existence and properties of constant mean curvature slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological constant, revealing multiple CMC slicings and their characteristics.
Contribution
It demonstrates that Kantowski-Sachs spacetimes can have multiple, diverse CMC slicings, contrasting with previous theorems applicable under different energy conditions.
Findings
Existence of multiple CMC slicings in certain Kantowski-Sachs spacetimes
Analysis of asymptotic properties of these slicings
Identification of conditions for unique or multiple CMC foliations
Abstract
We investigate existence, uniqueness, and the asymptotic properties of constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological constant. Since these spacetimes violate the strong energy condition, most of the general theorems on CMC slicings do not apply. Although there are in fact Kantowski-Sachs spacetimes with a unique CMC foliation or CMC time function, we prove that there also exist Kantowski-Sachs spacetimes with an arbitrary number of (families of) CMC slicings. The properties of these slicings are analyzed in some detail.
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