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Recent results in mathematical relativity
Piotr T. Chrusciel
We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorsh…
Gluing Initial Data Sets for General Relativity
Piotr T. Chrusciel, James Isenberg, Daniel Pollack
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data…
A poor man's positive energy theorem: II. Null geodesics
Piotr T. Chrusciel
We show that positivity of energy for stationary, or strongly uniformly Schwarzschildian, asymptotically flat, non-singular domains of outer communications can be proved using Gall…
Initial data engineering
Piotr T. Chrusciel, James Isenberg, Daniel Pollack
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the t…
KIDs are non-generic
R. Beig, P. T. Chrusciel, R. Schoen
We prove that generic solutions of the vacuum constraint Einstein equations do not possess any global or local space-time Killing vectors, on an asymptotically flat Cauchy surface,…
A poor man's positive energy theorem
Piotr T. Chrusciel, Gregory J. Galloway
We show that positivity of energy for stationary, asymptotically flat, non-singular domains of outer communications is a simple corollary of the Lorentzian splitting theorem.