This article is a guide to theorems on existence and global dynamics of solutions of the
Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy …

The most detailed existing proposal for the structure of spacetime singularities originates in
the work of Belinskii, Khalatnikov and Lifshitz. We show rigorously the correctness of this …

A graduate level text on a subject which brings together several areas of mathematics and
physics: partial differential equations, differential geometry and general relativity. It explains …

We use the Fuchsian algorithm to construct singular solutions of Einstein's equations which
belong to the class of Gowdy spacetimes. The solutions have the maximum number of …

This article is a guide to the literature on existence theorems for the Einstein equations
which also draws attention to open problems in the field. The local in time Cauchy problem …

We prove a stable blowup result for solutions to the Einstein-scalar field and Einstein-stiff
fluid systems. Our result applies to small perturbations of the spatially flat Friedmann …

There is increasing evidence that cosmological solutions exhibit rather special dynamical
behavior in the neighborhood of their singularities. The evidence is still essentially limited to …

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near
singularities. The technique has multiple applications including soliton theory, Einstein's …

Problem statement: The initiation of a detonation in an explosive gaseous mixture in the high
activation energy regime, in three space dimensions, typically leads to the formation of a …

We prove a stable singularity formation result for solutions to the Einstein-scalar field and
Einstein-stiff fluid systems. Our results apply to small perturbations of the spatially flat FLRW …