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

We solve the Euclidean Einstein equations with non-Abelian gauge fields of sufficiently large symmetry in various dimensions. In higher-dimensional spaces, we find the solutions which are similar to so-called scalar wormholes. In…

An affirmative answer is given to a conjecture of Myers concerning the existence of 5-dimensional regular static vacuum solutions that balance an infinite number of black holes, which have Kasner asymptotics. A variety of examples are…

A large class of solutions of the Einstein-conformal scalar equations in D=2+1 and D=3+1 is identified. They describe the collisions of asymptotic conformal scalar waves and are generated from Einstein-minimally coupled scalar spacetimes…

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…

We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…

In this letter we construct a new time-periodic solution of the vacuum Einstein's field equations whose Riemann curvature norm takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a…

We construct new classes of the dynamical black hole solutions in five or higher dimensional Einstein-Maxwell theory, coupled to a dilaton field, in the presence of arbitrary cosmological constant. The dilaton field interacts non-trivially…

We investigated the SU(2) Einstein-Yang-Mills system on a time-dependent non-diagonal cylindrical symmetric space-time. From the numerical investigation, wave-like solutions are found, consistent with the familiar string-like features. They…

We present solution generating techniques which permit to construct exact inhomogeneous and anisotropic cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimally interacting electromagnetic and…

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal…

We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology…

A technique is given to derive the well known Bell-Szekeres solution of the Einstein-Maxwell vacuum field equations describing the space-time and the Maxwell field following the head-on collision of two homogeneous, plane, electromagnetic…

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's…

We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but also relies strongly on certain geometric…

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a…

We construct hairy static black holes of higher dimensional general coupling Einstein-Skyrme theories with the scalar potential turned on and the cosmological constant is non-positive in which the scalar multiplets satisfy $O(d+1)$ model…

We consider solutions to the Einstein-massless-scalar field system with a positive cosmological constant, arising from sufficiently regular, near-FLRW, initial data. We establish global existence in the future direction and derive their…

Einstein-Maxwell equations with a cosmological constant are analyzed in a four dimensional stationary spacetime admitting in addition a two dimensional group $G_2$ of spatial isometries. Charged rotating open and closed black string…

We study spherically symmetric regular and black hole solutions in the Einstein-Skyrme theory with a negative cosmological constant. The Skyrme field configuration depends on the value of the cosmological constant in a similar manner to…

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…