J. Olivert

Relativistic Simultaneity and Causality

We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.

Rigid motions relative to an observer:L-rigidity

A new definition of rigidity,L-rigidity, in general relativity is proposed. This concept is a special class of pseudorigid motions and therefore it depends on the chosen curveL. It is shown that, for slow-rotation steady motions in Minkowski space, weak rigidity andL-rigidity are equivalent. The methods of the PPN approximation are considered. In this formalism, the equations that characterizeL-rigidity are expressed. As a consequence, the baryon mass density is constant in first order, the stress tensor is constant in the comoving system, the Newtonian potential is constant along the lineL, and the gravitational field is constant along the lineL in the comoving system.

A symplectic interpretation of some wave fronts in general relativity

In order to study the symplectic structures of the elementary relativistic free particles in general relativity, a nonvectorial associated fiber bundle is constructed over the space‐time manifold. A foliation in the space‐time is achieved which gives rise to the geodesics principle for massive particles and wave fronts for massless particles.

Noether's Theorem in Symplectic Bundles

After an analysis of some types of symplectic bundles, we use seeded fiberbundles to find laws of conservation in relativity from different dynamical groups.By using the concept of dynamical group in a bundle, we obtain an extensionof Noethers theorem to fiber bundle structures.

Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields

The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.

Presymplectic manifolds and conservation laws

In this paper we make use of a new structure called seeded fibre bundle. This allows us to combine the symplectic formalism and general relativity. A theorem of existence is obtained and some examples and properties are studied.

Symplectic Interpretation for the Discretization of Some Physical Magnitudes

We study some conditions for a pullback of asymplectic nonvectorial fiber bundle to have a discreteholonomy group. By applying this structure to therelativistic massless free particles for a hypersurface of simultaneity, and by using symplecticmechanics methods, we obtain that some physicalmagnitudes take discrete values.