相关论文: Future stability of the $1+3$ Milne model for Eins…

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that…

We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…

We prove the asymptotic stability of standing kink for the nonlinear relativistic wave equations of the Ginzburg-Landau type in one space dimension: for any odd initial condition in a small neighborhood of the kink, the solution,…

We study the equilibria of a self-gravitating scalar field in the region outside a reflecting barrier. By introducing a potential difference between the barrier and infinity, we create a kink which cannot decay to a zero energy state. In…

Minkowski space is shown to be globally stable as a solution to the massive Einstein--Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying…

In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by…

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows…

We construct growing mode solutions to the uncharged and charged Klein-Gordon equations on the sub-extremal Reissner-Nordstr\"om--anti-de-Sitter (AdS) spacetime under reflecting (Dirichlet or Neumann) boundary conditions. Our result applies…

We explore cosmological perturbations in a modified Gauss-Bonnet f(G) gravity, using a 1+3 covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear…

The stability of de Sitter metric in spacetimes where inflaton fields are non-minimally coupled to propagating torsion is investigated. It is shown that the de Sitter background metric is unstable against small perturbations. Axionic…

The 1+3 covariant equations, embedded in an extended tetrad formalism and describing a space-time with an arbitrary energy-momentum distribution, are reconsidered. It is shown that, provided the 1+3 splitting is performed with respect to a…

We prove that wave maps that factor as $\mathbb{R}^{1+d} \overset{\varphi_{\text{S}}}{\to} \mathbb{R} \overset{\varphi_{\text{I}}}{\to} M$, subject to a sign condition, are globally nonlinear stable under small compactly supported…

We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…

We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of…

In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full…

In the framework of an arbitrary $D$-dimensional metric theory, perturbations are considered on arbitrary backgrounds that are however solutions of the theory. Conserved currents for perturbations are presented following two known…

We consider the evolution of perturbed cosmological spacetime with multiple scalar fields in Einstein gravity. A complete set of scalar-type perturbation equations is presented in a gauge-ready form, and we derived the closed set of…

The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…

In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…