3 Foliations

The components of a Gowdy metric, see Equations (2View Equation) and (3View Equation), are not explicit functions of the coordinates. However, imposing Einstein’s equations leads to a system of nonlinear wave equations for the components. Consequently, it is useful to analyze the asymptotic behavior of the solutions to this system in order to be able to draw conclusions concerning the global geometry of the corresponding spacetimes. One natural first question to ask is if there are any preferred global foliations. Is there, e.g., a constant mean curvature (CMC) foliation?

 3.1 CMC foliations
 3.2 Areal foliation
 3.3 Existence of foliations, related symmetry classes
 3.4 Prescribed mean curvature

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