One studies the differential equations of the movement of certain classical and relativistic systems for some special Lagrangian functions. One considers particularly the case in which the problem presents cyclic coordinates. Some electrodynamical applications are studied.
A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post-Newtonian order.
Il lavoro deduce, in ambito relativistico, le proprietà fondamentali di un flusso luminoso (congruenza nulla) mediante tecniche anolonome reali [2,3] e precisamente: caratteristiche geometrico-cinematiche del flusso (assolute e relative), teorema di Sachs [6] e proprietà dei nastri luminosi, con particolare riguardo ai parametri ottici e di deformazione, in spazi-tempo particolari (stazionarietà relativa, flussi geodetici, riferimenti trasportati per parallelismo dalla luce).
Dynamics of a point-particle system interacting gravitationally according to the general theory of relativity can be analyzed within the canonical formalism of Arnowitt, Deser, and Misner. To describe the property of being a point particle one can employ Dirac delta distribution in the energy-momentum tensor of the system. We report some mathematical difficulties which arise in deriving the 3rd post-Newtonian Hamilton's function for such a system. We also offer ways to overcome partially these difficulties....
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .