Global properties of higher-dimensional cosmological spacetimes

TL;DR

This paper proves global existence and analyzes the asymptotic behavior of higher-dimensional inhomogeneous cosmological spacetimes within the Einstein-Maxwell-dilaton system, extending understanding of singularities and spacetime evolution.

Contribution

It establishes global existence theorems for higher-dimensional Einstein-Maxwell-dilaton spacetimes and analyzes their singularity structures, including velocity-term dominated singularities.

Findings

Global existence of solutions in areal and constant mean curvature time coordinates.

Existence of asymptotically velocity-term dominated singularities in vacuum Einstein gravity.

Results hold for both analytic and smooth free functions.

Abstract

We study global existence problems and asymptotic behavior of higher-dimensional inhomogeneous spacetimes with a compact Cauchy surface in the Einstein-Maxwell-dilaton (EMD) system. Spacelike $T^{D-2}$-symmetry is assumed, where $D\geq 4$ 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-terms dominated singularities in the both cases which free functions are analytic and smooth.