相关论文: On periodic solutions of nonlinear wave equations,…

We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…

We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…

Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…

We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…

We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the `compact' extra dimension, and their conformal infinity is the…

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…

We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…

In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is…

We prove the existence of infinitely many classical periodic solutions for a class of semilinear wave equations with periodic boundary conditions. Our argument relies on some new estimates for the linear problem with periodic boundary…

A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the…

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…

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…

We argue that the Einstein-Yang-Mills theory presents nontrivial solutions with a NUT charge. These solutions approach asymptotically the Taub-NUT spacetime. They are characterized by the NUT parameter, the mass and the node numbers of the…

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the…

We study the dynamics of two-component Bose-Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary…

We construct one-parameter families of solutions to the Einstein--Klein--Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole…

Motivated by the study of small amplitudes non-linear waves in the Anti-de-Sitter spacetime and in particular the conjectured existence of periodic in time solutions to the Einstein equations, we construct families of arbitrary small…

We study the classical solutions of the Einstein-Yang-Mills model in five dimensions in the presence of a cosmological constant $\Lambda$. Using a spherically symmetric ansatz and assuming that the fields do not depend on the extra…

We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…

We consider a class of ans\"atze for the construction of exact solutions of the Einstein-nonlinear $\sigma$-model system with an arbitrary cosmological constant in (3+1) dimensions. Exploiting a geometric interplay between the $SU(2)$ field…