Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Huneau, Cecile"'
Autor:
Huneau, Cécile, Luk, Jonathan
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact characterization o
Externí odkaz:
http://arxiv.org/abs/2404.07659
Autor:
Huneau, Cécile, Luk, Jonathan
We prove Burnett's conjecture in general relativity when the metrics satisfy a generalized wave coordinate condition, i.e., suppose $\{g_n\}_{n=1}^\infty$ is a sequence of Lorentzian metrics (in arbitrary dimensions $d \geq 3$) satisfying a generaliz
Externí odkaz:
http://arxiv.org/abs/2403.03470
In this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in $\m R^{1+4}$ with one direction compactified on a circle. We consider small perturbations which are allowed to vary i
Externí odkaz:
http://arxiv.org/abs/2307.15267
Autor:
Huneau, Cécile, Vâlcu, Caterina
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the conformal m
Externí odkaz:
http://arxiv.org/abs/2111.14395
Autor:
Huneau, Cécile, Stingo, Annalaura
Publikováno v:
Analysis & PDE 17 (2024) 2033-2075
We consider a system of quasilinear wave equations on the product space $\mathbb{R}^{1+3}\times \mathbb{S}^1$, which we want to see as a toy model for Einstein equations with additional compact dimensions. We show global existence for small and regul
Externí odkaz:
http://arxiv.org/abs/2110.13982
Autor:
Huneau, Cécile, Luk, Jonathan
Consider a sequence of $C^4$ Lorentzian metrics $\{h_n\}_{n=1}^{+\infty}$ on a manifold $\mathcal M$ satisfying the Einstein vacuum equation $\mathrm{Ric}(h_n)=0$. Suppose there exists a smooth Lorentzian metric $h_0$ on $\mathcal M$ such that $h_n\t
Externí odkaz:
http://arxiv.org/abs/1907.10743
Autor:
Huneau, Cécile, Luk, Jonathan
Publikováno v:
Duke Math. J. 167, no. 18 (2018), 3315-3402
Known examples in plane symmetry or Gowdy symmetry show that given a $1$-parameter family of solutions to the vacuum Einstein equations, it may have a weak limit which does not satisfy the vacuum equations, but instead has a non-trivial stress-energy
Externí odkaz:
http://arxiv.org/abs/1706.09501
Autor:
Huneau, Cécile, Luk, Jonathan
We prove local existence of solutions to the Einstein--null dust system under polarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one can identify
Externí odkaz:
http://arxiv.org/abs/1706.09499
Autor:
Häfner, Dietrich, Huneau, Cécile
We consider the spherically symmetric SU(2) Yang-Mills Fields on the Schwarzschild metric. Within the so called purely magnetic Ansatz we show that there exists a countable number of stationary solutions which are all nonlinearly unstable.
Externí odkaz:
http://arxiv.org/abs/1612.06596
Autor:
Huneau, Cécile
In this paper we prove the nonlinear stability of Minkowski space-time with a translation Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein equations with a scalar field. We work in ge
Externí odkaz:
http://arxiv.org/abs/1511.07002