Abstract
We study global existence problems and asymptotic behaviour of higher-dimensional inhomogeneous spacetimes with a compact Cauchy surface in the Einstein–Maxwell–dilaton (EMD) system. Spacelike TD−2 symmetry is assumed, where D ⩾ 4 is spacetime dimension. The system of the evolution equations of the EMD equations in the areal time coordinate is reduced to a wave map system, and a global existence theorem for the system is shown. As a corollary of this theorem, a global existence theorem in the constant mean curvature time coordinate is obtained. Finally, for vacuum Einstein gravity in arbitrary dimension, we show existence theorems of asymptotically velocity-term-dominated singularities in both cases in which free functions are analytic and smooth.
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