Displaying similar documents to “The global nonlinear stability of the Minkowski space”

Projective relatedness and conformal flatness

Graham Hall (2012)

Open Mathematics

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This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential...

Polyhomogeneous solutions of wave equations in the radiation regime

Piotr T. Chruściel, Olivier Lengard (2000)

Journées équations aux dérivées partielles

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While the physical properties of the gravitational field in the radiation regime are reasonably well understood, several mathematical questions remain unanswered. The question here is that of existence and properties of gravitational fields with asymptotic behavior compatible with existence of gravitational radiation. A framework to study those questions has been proposed by R. Penrose (R. Penrose, “Zero rest-mass fields including gravitation”, Proc. Roy. Soc. London A284 (1965), 159-203),...

Einstein-Euler equations for matter spacetimes with Gowdy symmetry

Philippe G. LeFloch (2008-2009)

Séminaire Équations aux dérivées partielles

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We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T 3 . Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit,...