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A general analytic spherically symmetric solution of the Bogomol'nyi equations is found. It depends on two constants and one arbitrary function on radius and contains the Bogomol'nyi-Prasad-Sommerfield and Singleton solutions as particular…

A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…

The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…

According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…

The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…

The Gauss-Bonnet density `a la Palatini' is not a total derivative in four dimensions. We study spherically symmetric fields for the torsion-free theory. The resulting equations are highly complicated but we show the existence of unexpected…

Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of…

We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…

We consider an Einstein-Yang-Mills Lagrangian in a five dimensional space-time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional…

In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have…

It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…

It is shown that, somewhat similar to the case of classical Baecklund transformations for surfaces of constant negative curvature, infinitely many axially symmetric minimal hypersurfaces in 4-dimensional Minkowski-space can be obtained, in…

In this article we find explicit formulae for spherically symmetric solutions of the multidimensional zero-pressure gas dynamics system and its adhesion approximation. The asymptotic behaviour of the explicit solutions of the adhesion…

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild…

We expound in detail a method frequently used to reduce the Dirac equation in D-dimensional (D >= 4) spherically symmetric spacetimes to a pair of coupled partial differential equations in two variables. As a simple application of these…

In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the…

The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and…

Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus…

Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with nonlinear term of the form sign(\phi) are presented. They are constructed from cubic polynomials in the scale invariant variable t/r. One…

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…