Tensorial Euler-Lagrange expressions and conservation laws.
Tensorial Euler-Lagrange expressions and conservation laws. (Short Communication).
The global nonlinear stability of the Minkowski space
The homological Kähler-de Rham differential mechanism. I: Application in general theory of relativity.
The instability of naked singularities in the gravitational collapse of a scalar field.
The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant
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 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 , the background metric + fluid solutions...
The quantum spheres and their embedding into quantum Minkowski space-time.
The resolution of the bounded curvature conjecture in general relativity
This paper reports on the recent proof of the bounded curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.
The structure of the space of solutions of Einstein's equations. I. One Killing field
Travelling wave solutions to some PDEs of mathematical physics.
TT-tensors and conformally flat structures on 3-manifolds
We study TT-tensors on conformally flat 3-manifolds (M,g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when M is simply connected and has vanishing 2nd de Rham cohomology.
Weakly regular -symmetric spacetimes. The global geometry of future Cauchy developments
We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...
Well posed reduced systems for the Einstein equations
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.
Об интегрировании уравнений Эйнштейна методом обратной задачи теории рассеяния
Хроногеометрия многообразий Геделя и де Ситтера