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We present cylindrically symmetric solutions for a type of the Gauss-Bonnet gravity, in details. We derive the full system of the field equations and show that there exist seven families of exact solutions for three forms of viable models.…
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…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
The solution generating methods discovered earlier for integrable reductions of Einstein's and Einstein - Maxwell field equations (such as soliton generating techniques, B$\ddot{a}$cklund or symmetry transformations and other…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
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 impose in the nonsymmetric gravitational theory, by means of Lagrange multiplier fields in the action, a set of covariant constraints on the antisymmetric tensor field. The canonical Hamiltonian constraints in the weak field…
Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broadband…
We investigate the Zipoy-Voorhees metric ($q-$metric) as the simplest static, axially symmetric solution of Einstein's vacuum field equations that possesses as independent parameters the mass and the quadrupole moment. In accordance with…
Gravitational vector degrees of freedom typically arise in many examples of modified gravity models. We start to systematically explore their role in these scenarios, studying the effects of coupling gravitational vector and scalar degrees…
Just recently, the class of all Einstein-Maxwell fields solving simultaneously also any higher-order modification of the Eintein-Maxwell theory has been completely identified. In the present work, we argue that, in view of our recent…
A spherically symmetric monopole solution is found in SO(5) gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski spacetime. The action of the Yang-Mills fields is quartic in field strengths. The…
From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity the uniqueness of wide families of exact solutions is established, among them, all…
In higher dimensional gauge theory, we need energies with higher power terms of field strength in order to realize point-wise monopoles. We consider new models with higher power terms of field strength and extraordinary kinetic term of…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Supersymmetric instanton solutions in four dimensional Euclidean ungauged Einstein-Maxwell theory are analysed and classified according to the fraction of supersymmetry they preserve, using spinorial geometry techniques.
We present new classical solutions of Einstein-Yang-Mills-Higgs theory, representing gravitating sphaleron-antisphaleron pair, chain and vortex ring solutions. In these static axially symmetric solutions, the Higgs field vanishes on…
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 gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that…
The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is given by the source vertical tangent bundle restricted to the identity bisection. Its sections can be identified with the invariant vector…