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Quasi-local energy-momentum and the Sen geometry of two-surfaces

László Szabados (1997)

Banach Center Publications

We review the main ideas of the two dimensional Sen geometry and apply these concepts i. in finding the `most natural' quasi-local energy-momentum, ii. in characterizing the zero energy-momentum and zero mass configurations and iii. in finding the quasi-local radiative modes of general relativity.

Regularity and geometric properties of solutions of the Einstein-Vacuum equations

Sergiu Klainerman, Igor Rodnianski (2002)

Journées équations aux dérivées partielles

We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of...

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