Fuchsian methods and spacetime singularities

Abstract

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated.

References in corpus (9)

• Numerical Approaches to Spacetime Singularities
• Analytic description of singularities in Gowdy spacetimes
• On the Einstein-Vlasov system with hyperbolic symmetry
• Manufacture of Gowdy spacetimes with spikes
• Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry
• Asymptotic Behavior of Polarized and Half-Polarized U(1) symmetric Vacuum Spacetimes
• Isotropic cosmological singularities: other matter models
• Asymptotic Behavior in Polarized {\bf T}${}^2$-symmetric Vacuum Spacetimes
• Fuchsian analysis of S^2xS^1 and S^3 Gowdy spacetimes

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• Stationary Black Holes as Holographs
• On the backward stability of the Schwarzschild black hole singularity
• Space-time extensions II
• The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison