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To model magnetic fields of compact objects we solve the Maxwell equations in the background of the exterior static Schwarzschild and slowly rotating Kerr space-times. We impose the boundary condition that the electromagnetic fields are to…
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate…
We consider the Einstein-Yang-Mills-Higgs equations for an SU(3) gauge group in a spherically symmetric ansatz. Several properties of the gravitating monopole solutions are obtained an compared with their SU(2) counterpart.
One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish…
Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to…
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…
This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional Lie algebras that arise in the context of asymptotic symmetries of…
Spherical clusters of SU(2) BPS monopoles are investigated here. A large class of monopole solutions is found using an abelian approximation, where the clusters are spherically symmetric, although exact solutions cannot have this symmetry…
An algorithm is proposed for research into the symmetrical properties of theoretical and mathematical physics equations. The application of this algorithm to the free Schrodinger equation permited us to establish that in addition to the…
The $f(R)$ theory is considered for static cylindrically symmetric and plane-symmetric spacetimes. In order to find solutions to the field equations of these models, the Noether symmetry method is used. First, we examine the GR case for…
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analogue models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation,…
This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…