  Gravitational properties of a hedge-hog type topological defect in two extra
dimensions are considered in General Relativity employing a vector as the order
parameter. All previous considerations were done using the order parameter in
the form of a multiplet in a target space of scalar fields. The difference of
these two approaches is analyzed and demonstrated in detail. Regular solutions
of the Einstein equations are studied analytically and numerically. It is shown
that the existence of a negative cosmological constant is sufficient for the
spontaneous symmetry breaking of the initially plain bulk. Regular
configurations have a growing gravitational potential and are able to trap the
matter on the brane. If the energy of spontaneous symmetry breaking is high,
the gravitational potential has several points of minimum. Identical in the
uniform bulk spin-less particles, being trapped within separate minima, acquire
different masses and appear to the observer on brane as different particles
with integer spins.

General Relativity and Quantum Cosmology