### Hyperbolic methods for Einstein's equations.

Reula, Oscar A. (1998)

Living Reviews in Relativity [electronic only]

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Reula, Oscar A. (1998)

Living Reviews in Relativity [electronic only]

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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,...

Berger, Beverly K. (2002)

Living Reviews in Relativity [electronic only]

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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),...

Alan Rendall (1997)

Banach Center Publications

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Dennis M. DeTurck (1983)

Compositio Mathematica

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Yvonne Choquet-Bruhat, James York (1997)

Banach Center Publications

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We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.

Raffe Mazzeo (1999)

Journées équations aux dérivées partielles

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In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor $D$. We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical...