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Einstein-Euler equations for matter spacetimes with Gowdy symmetry

Philippe G. LeFloch (2008/2009)

Séminaire Équations aux dérivées partielles

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, both, impulsive...

Solutions globales des équations d’Einstein-Maxwell

Julien Loizelet (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

En adaptant une méthode de Lindblad et Rodnianski, on prouve l’existence de solutions globales pour les équations d’Einstein-Maxwell en dimension d’espace n 3 . Les données initiales considérées sont lisses, asymptotiquement euclidiennes et suffisamment petites. On utilise la jauge harmonique et la jauge de Lorenz.

Special Einstein’s equations on Kähler manifolds

Irena Hinterleitner, Volodymyr Kiosak (2010)

Archivum Mathematicum

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.

The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant

Igor Rodnianski, Jared Speck (2013)

Journal of the European Mathematical Society

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c 2 ρ , 0 < c 2 < 1 / 3 , the background metric + fluid solutions...

The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

Jonathan Luk (2013)

Journal of the European Mathematical Society

We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region { r t 4 } .

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