By describing the dynamical evolution of a test charged particle in the presence of an electromagnetic field as a succession of infinitesimal Lorentz boosts and rotations it is possible to obtain the Lorentz Force of Electrodynamics. A consequence of this derivation at the classical level is that, given the existence of electric and magnetic fields, the form of the electromagnetic force acting on the particle can be regarded as arising from the geometry of Minkowskian spacetime.
The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are found. The manifold admits a four-parameter groups of motions that act nontransitively on the spacetime. All admissible electromagnetic fields for which such algebras exist are found. In the case of an arbitrary n-dimensional Riemannian space on which the group of motions acts, it is proved that the admissible field does not deform the algebra of symmetry operators of the free Hamilton-Jacobi and Klein…
We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein--Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is stat…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists three classes of such $r$-matrices, one of them being a novel two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces corresponding to these three deformations are explicitly constructed in both local and ambient coordinates. Their quantization is performed, thus giving rise to the associated noncommutative spacetimes, that in the Minkowski case a…
We derive the equations governing the linear stability of Kerr-Newman spacetime to coupled electromagnetic-gravitational perturbations. The equations generalize the celebrated Teukolsky equation for curvature perturbations of Kerr, and the Regge-Wheeler equation for metric perturbations of Reissner-Nordström. Because of the "apparent indissolubility of the coupling between the spin-1 and spin-2 fields", as put by Chandrasekhar, the stability of Kerr-Newman spacetime can not be obtained through standard decomposition in modes. Due to the impossibility to decouple the modes of the gravitational …
We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, $ |\mathcal{Q}|=M, $ Reissner-Nordström spacetime, as a solution to the Einstein-Maxwell equations. Our work uses and extends the framework \cite{giorgi2019boundedness,giorgie2020boundedness} of Giorgi, and contrary to the subextremal case we prove that instability results hold for a set of gauge invariant quantities along the event horizon $ \mathcal{H}^+ $. In particular, we prove decay, non-decay, and polynomial blow-up estimates asymptotically along $ \mathcal{H}^+ $, the exact behavio…
