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A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
Using a recently developed generalized Weyl formalism, we construct an asymptotically flat, static vacuum Einstein solution that describes a superposition of multiple five-dimensional Schwarzschild black holes. The spacetime exhibits a…
The coupled Einstein-Yang-Mills equations on a time dependent axially symmetric spacetime are investigated, without a priori any conditions on the gauge field. There is numerical evidence for the existence of a regular solution with the…
We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
The axisymmetric static solution of Born-Infeld nonlinear electrodynamics with ring singularity is investigated. This solution is considered as a static part of massive charged particle with spin and magnetic moment. The method for…
For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
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…
We investigate gravitational properties of thin planar wall solutions of the Einstein's equations in the weak field approximation. We find the general metric solutions and discuss the behavior of a particle placed initially at rest to one…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can…
One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
Nonlinear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are…
The static solutions of the axially symmetric vacuum Einstein equations with a finite number of Relativistic Multipole Moments are described by means of a function that can be written in the same analytic form as the Newtonian gravitational…