Related papers: Generalized Metrical Multi-Time Lagrange Geometry …
The paper construct a suitable generalized metrical multi-time Lagrange geometrical model for both gravitational and electromagnetic fields, in a general setting. In this construction, the gravitational potentials are described by a…
The author exposes the metrical multi-time Lagrange geometry of physical fields which naturally generalizes the classical Lagrangian developped by Miron and Anastasiei. In other words, one constructs a natural theory of physical fields on…
In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and…
A geometrization of a Kronecker $h$-regular multi-time Lagrangian function with partial derivatives of order one is described, in the sense of d-connections, d-torsions and d-curvatures.
The aim of this paper is to develop on the 1-jet space J^1(R,M^4) the jet Generalized Lagrange Geometry for the rheonomic Chernov metric. The associated gravitational and electromagnetic field models based on the rheonomic Finsler Chernov…
In a previous paper, we have introduced a new unified description of the main equations of the gravitational and of the electromagnetic field, in terms of tidal tensors and connections on the tangent bundle TM of the space-time manifold. In…
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is…
The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle $J^{1*}(\cal{T},M)$ (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
We study Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell's field.
We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes.…
By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the…
We add some comments to our old paper \cite{F-U} where the metric tensor was introduced as the gauge theory of general coordinate transformation. This formulation is more satisfactorily completed than the original one if it is required to…
In this paper we will extend the notion of tangent bundle to a $\z$ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-riemannian metrics, Levi-civita connection, and curvature, on it. In…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…