Related papers: Non-linear constitutive equations for gravitoelect…
A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property,…
We outline a new geometric method of constructing exact solutions of gravitational field equations parametrized by generic off-diagonal metrics, anholonomic frames and possessing, in general, nontrivial torsion and nonmetricity. The…
We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish.…
In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and…
In this paper we study the quantum wave packet of the non-linear Gross-Pitaevskii equation.
The full non-linear structure of the action and transformation rules for $\W_N$-gravity coupled to matter are obtained from a non-linear truncation of those for $w_ \infty$ gravity. The geometry of the construction is discussed, and it is…
We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler-Heisenberg non-linear electrodynamics. For these solutions, we determine the non-commutative corrections to the horizon radius for the…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
It is argued that once we consider the underpinning of a Non Commutative geometry, itself symptomatic of extended particles, for example in Quantum Superstring theory, then a reconciliation between gravitation and electromagnetism is…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.
We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into General Relativity (GR) coupled to another nonlinear theory of…
A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…
At first, we discuss parallels electric and magnetic fields solutions in a gravitational background. Then, considering eletromagnetic and gravitational waves symmetries we show a particular solution for stationary gravitational waves.…
We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the…
This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory…
A method for obtaining the constitutive equations for describing the simple nonpolar continuum media is given. The method is based on the theory of Lie groups and on group properties of the differential equations.