FIELD EQUATIONS FOR SPACE–TIME–MATTER THEORY

In the present paper we obtain, in a covariant form, and in their full generality, the field equations in a relativistic general Kaluza–Klein space. This is done by using the Riemannian horizontal connection defined in [3], and some 4D horizontal tensor fields, as for instance: horizontal Ricci tensor, horizontal Einstein gravitational tensor field, horizontal electromagnetic energy–momentum tensor field, etc. Also, we present some inter-relations between STM theory and brane-world theory. This enables us to introduce in brane theory some electromagnetic potentials constructed by means of the warp function.

BLACK HOLES AND BLACK STRING-LIKE SOLUTIONS IN CODIMENSION-2 BRANEWORLDS

We discuss black hole solutions with a Gauss-Bonnet term in the bulk and an induced gravity term on a thin brane of codimension-2. We show that these black holes can be localized on the brane, and they can be extended further into the bulk by a warp function. These solutions have regular horizons and no other curvature singularities appear apart from the string-like ones. The projection of the Gauss-Bonnet term on the brane imposes a constraint relation which dictates the form of matter on the brane and in the bulk.

Natural brane-confinement from massive Z 2-spontaneously broken Kaluza-Klein excitations in the bulk

For a real scalar field minimally coupled to bulk gravity, in five dimensions, we analytically solve the Gordon equation, near one of the degenerated vacua of an effective potential with a spontaneously broken Z 2-symmetry. Dealing with the back-reaction from the excited massive modes on the whole scale function, we are pointing out that the lighter excitations of the scalar in the bulk turn more and more the warp function into the one of a partition on the confined brane.