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By extending the notion of Lie derivative to distribution-valued tensor fields of order $m$, Lie derivatives with respect to $C^k$ vector fields, $k\geqslant m+1$, can be shown to be well defined. Geometric symmetries, definable in terms of…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein…
We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for…
Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family of the actions for two-dimensional gravity (in particular, string-inspired models) is investigated. Charged black holes which appear in the theory are briefly…
For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov~I~type spacetimes, which do not arise in models of the general theory of relativity. The theory of gravity under…
Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modelling of the expected signals in extensions of General Relativity. In this paper we…
Exact solutions of the Wheeler-DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schr\"odinger wavefunctionals having support on 3-metrics of constant spatial…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially…
Detection of gravitational waves (GW) opened new windows on fundamental physics and it would be natural to search how the role of extra dimensional effects can be traced to gravitational wave physics. In this article, we consider a toy…
We analyze the coset model $(E_2^c \ti E_2^c)/E_2^c$ and construct a class of exact string vacua which describe plane gravitational waves and their duals, generalizing the plane wave background found by Nappi and Witten. In particular, the…
A non-minimal coupling of Weyl curvatures to electromagnetic fields is considered in Brans-Dicke-Maxwell theory. The gravitational field equations are formulated in a Riemannian spacetime where the spacetime torsion is constrained to zero…
For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
All classes of spatially homogeneous space-time models in the generalized scalar-tensor theory of gravity are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of %complete…
We present a new class of magnetic brane solutions in $(n+1)$-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our…
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to…