Confinamento geodésico clássico em espaço produto distorcido

Abstract

In this dissertation our main objective is to study the classical geodesic motions of nonzero rest mass test particles and photons in five-dimensional warped product spaces. We show that it is possible to obtain a general picture of these mo- tions, using the natural decoupling that occurs in such spaces between the motions in the fifth dimension and the motion in the hypersurfaces. This splitting allows the use of phase space analysis in order to investigate the possible confinement of particles and photons to hypersurfaces in five-dimensional warped product spaces. Using such analysis, we find a novel form of quasi-confiment which is oscillatory and neutrally stable. The importance of such a confiment is that it is purely due to the classical gravitational e¤ects, without requiring the presence of brane-type confinement mechanisms. We then extend this procedure to study the classical geo- desic motions of nonzero rest mass test particles and photons in the more general case of a (3 + 1 + n)-dimensional warped product spaces. Again, an important feature of these spaces is that they allow a natural decoupling between the motions in the (3 + 1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling once more and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3 + 1)- spacetime sub- manifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of semi-riemannian manifolds as well as establishing the conditions for the stability of such confinement.