相关论文: Global Non-Linearly Stable Large-Data Solutions to…
We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
We study solutions to the Einstein equations coupled to a nonlinear scalar field with exponential potential. This system admits Friedmann-Lema\^itre-Robertson-Walker solutions undergoing decelerated expansion, with $\mathbb{T}^3$ spatial…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
In this paper, we study the future causally geodesically complete solutions of the spherically symmetric Einstein-scalar field system. Under the a priori assumption that the scalar field $\phi$ scatters locally in the scale-invariant…
We construct semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no oscillations due to…
We show that the spherically symmetric Einstein-scalar-field equations for small slowly particle-like decaying initial data at null infinity have unique global solutions.
We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's…
We linearize the Einstein-scalar field equations, expressed relative to constant mean curvature (CMC)-transported spatial coordinates gauge, around members of the well-known family of Kasner solutions on $(0,\infty) \times \mathbb{T}^3$.…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…
We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…
We show that the maximal globally hyperbolic development of near-FLRW initial data for the Einstein scalar-field Vlasov system exhibits stable Big Bang formation in the collapsing direction. The solutions exhibit stable Kretschmann scalar…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
First we review some of the attempts made to find exact spherically symmetric solutions of Einstein field equations in the presence of scalar fields .Wyman solution in both static and non static scalar field is discussed briefly and it is…
This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and…
We prove the nonlinear stability in the contracting direction of Friedmann-Lema\^itre-Robertson-Walker (FLRW) solutions to the Einstein-scalar field equations in $n\geq 3$ spacetime dimensions that are defined on spacetime manifolds of the…
We consider the Einstein-Dirac system for a massive field, which describes the evolution of self-gravitating massive spinor fields, and we investigate the global evolution problem, when the initial data set is sufficiently close to data…
General static solutions of effectively 2-dimensional Einstein-Dilaton-Maxwell-Scalar theories are obtained. Our model action includes a class of 2-d dilaton gravity theories coupled with a $U(1)$ gauge field and a massless scalar field.…
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…