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The Penrose Inequality
Hubert L. Bray, Piotr T. Chrusciel
In 1973, R. Penrose presented an argument that the total mass of a space-time which contains black holes with event horizons of total area should be at least . An…
Manifold structures for sets of solutions of the general relativistic constraint equations
Piotr T. Chrusciel, Erwann Delay
We construct manifold structures on various sets of solutions of the general relativistic initial data sets.
On the dynamics of Gowdy space times
Myeongju Chae, Piotr T. Chrusciel
We study the behavior near the singularity t=0 of Gowdy metrics. We prove existence of an open dense set of boundary points near which the solution is smoothly "asymptotically velo…
On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
Piotr T. Chrusciel, Erwann Delay
Generalising an analysis of Corvino and Schoen, we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces. As a corol…