Related papers: Stationary multiple euclidon solutions to the vacu…
Stationary, axisymmetric and slowly rotating vacuum spacetimes in the Ho\v{r}ava-Lifshitz (HL) gravity are studied, and shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
In present article effective nonlinear sigma model (NSM) is considered. Einstein equation solution, corresponded to the chiral fields determined by functional parameter method, are presented. Effective NSM of stationary axially-symmetric…
We consider methods for constructing explicit solutions of the non-stationary Lam\'e equation, which is a generalization of the classical Lam\'e equation, that has appeared in works on integrable models, conformal field theory, high energy…
We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution…
The charged, spinning and gravitating soliton is realized as a regular solution of the Kerr-Newman field coupled with a chiral Higgs model. A regular core of the solution is formed by a domain wall bubble interpolating between the external…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
It is shown that the 4D Einstein-Klein-Gordon equations with a phantom scalar field (a scalar field with a negative sign in front of the kinetic energy term of its Lagrange density) has non-singular, spherically symmetry solutions. These…
We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than one stagnation point. These solutions are also homogeneous…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
We analyse the expression for the mass of a stationary axisymmetric configuration in general relativity obtained in our previous work [1]. From the generality of our formula and its incompatibility with the corresponding expression in Kerr…
A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars (Skyrme model). This solution corresponds to a spacetime defect and its construction…
This paper generalizes two previously known techniques for generating minimally coupled Einstein-scalar field solutions in 4 dimensions; the Buchdahl and Fonarev transformations. By applying this solution generation technique, minimally…
In this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the density and one for the evolution of a mean field potential. We…