On de Sitter-like and Minkowski-like space-times

Abstract

Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge the location of the conformal boundary of the space-times is known \emph{a priori} once the initial data has been prescribed. Thus it provides an analysis which is conceptually and calculationally simpler.

24 pages, typos corrected to match published version in CQG

References in corpus (6)

• Existence and stability of even dimensional asymptotically de Sitter spaces
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
• Conformal geodesics on vacuum space-times
• Asymptotic analysis of ultra-relativistic charge
• Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT
• Multiple currents in charged beams

Cited by in corpus (13)

• A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
• The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field
• Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations
• A rigidity property of asymptotically simple spacetimes arising from conformally flat data
• Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class
• Linearised conformal Einstein field equations
• Spectral methods for the spin-2 equation near the cylinder at spatial infinity
• On the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes
• Conformal geodesics in spherically symmetric vacuum spacetimes with Cosmological constant
• On the non-linear stability of the Cosmological region of the Schwarzschild-de Sitter spacetime
• A conformal approach to the stability of Einstein spaces with spatial sections of negative scalar curvature
• The conformal Einstein field equations and the local extension of future null infinity
• The space spinor formalism and estimates for spinor fields