Weakly regular \(T^2\)-symmetric spacetimes. The future causal geometry of Gowdy spacetimes
The Gowdy spacetimes play a role of an important toy model for dynamical problems of cosmology, including the standard Big Bang model, since they allows an analytical consideration of non-trivial non-stationary phenomena. Here, the authors focus their attention on a global causal structure in the sense of distributions considering global future geometry of spacetimes with general \(T^2\) symmetry within the weak version of the Einstein equations defined geometrically. The principal result of this work, the proof of future timelike geodesically completeness for the weakly regular Gowdy spacetimes, is based on several steps highlighting new features of the model: the correction term controlled by the energy is introduced to obtain new energy functional, avoiding high-order derivatives and pointwise estimates of Christoffel symbols.
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