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- W2106301787 abstract "The present thesis is concerned with the construction of Gowdy spacetimes with torus topology in n dimensions and the study of their asymptotics as t → ∞. Already much is known about these spaces in four dimensions, in particular, the solution to Einstein’s vacuum equations can be represented as a wave-map from a Minkowski-like space to the hyperbolic plane whose energy decays as t−1 as t → ∞. The behaviour of the solution at large times is governed by a quantity which is invariant under isometries of the target-space. The present thesis contains a derivation of the target-space metric in the general case, i. e., the standard metric on SL(n − 2)/SO(n − 2) in certain coordinates, and shows that, just as in four dimensions, the energy of the wave-map which describes the solution decays as t−1 as t → ∞. A quantity analogous to the invariant in four dimensions is constructed from time-conserved quantities. For homogeneous data, this invariant is, at fixed time, proportional to the kinetic energy of the wave-map." @default.
- W2106301787 created "2016-06-24" @default.
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- W2106301787 date "2010-01-01" @default.
- W2106301787 modified "2023-09-26" @default.
- W2106301787 title "Energy Decay Law in n-Dimensional Gowdy Spacetimes with Torus Topology" @default.
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