Vector order parameter in general relativity. Covariant equations

Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are derived. The topological defects are classified in accordance with the symmetry of the covariant derivative of the vector order parameter. The abilities of the derived equations are demonstrated in application to the brane world concept. New solutions of the Einstein equations with a transverse vector order parameter are presented. In the vicinity of phase transition the solutions are found analytically

To the theory of the Universe evolution

Self-consistent account of the most simple non-gauge vector fields leads to a broad spectrum of regular scenarios of temporal evolution of the Universe completely within the frames of the Einstein's General relativity. The longitudinal non-gauge vector field is "the missing link in the chain", displaying the repulsive elasticity and allowing the macroscopic description of the main features of the Universe evolution. The singular Big Bang turns into a regular inflation-like state of maximum compression with the further accelerated expansion at late times. The parametric freedom of the theory allows to forget the troubles of fine tuning. In the most interesting cases the analytical solutions of the Einstein's equations are found.Comment: 25 pages, 9figure

Bose-Einstein Condensate in Synchronous Coordinates

Analytical spherically symmetric static solution to the set of Einstein and Klein-Gordon equations in a synchronous reference frame is considered. In a synchronous reference frame, a static solution exists in the ultrarelativistic limit p=−ε/3. Pressure p is negative when matter tends to contract. The solution pretends to describe a collapsed black hole. The balance at the boundary with dark matter ensures the static solution for a black hole. There is a spherical layer inside a black hole between two “gravitational” radii rg and rh>rg, where the solution exists, but it is not unique. In a synchronous reference frame, detgik and grr do not change signs. The non-uniqueness of solutions with boundary conditions at r=rg and r=rh makes it possible to find the gravitational field both inside and outside a black hole. The synchronous reference frame allows one to find the remaining mass of the condensate. In the model “λψ4”, total mass M=3c2/2k rh is three times that of what a distant observer sees. This gravitational mass defect is spent for bosons to be in the bound ground state, and for the balance between elasticity and density of the condensate

Global topological defects in extra dimensions and the brane world concept

Summary: "D-dimensional (Dgeq5) configurations with 4D Minkowski external space-time and global spherically symmetric topological defects in the extra dimensions are discussed in the context of the brane world concept. The defect is formed with a hedgehog-like set of scalar fields phi^i with a symmetry-breaking potential V depending on the magnitude phi^2=phi^iphi^i. All possible kinds of globally regular configurations are singled out without specifying the shape of V(phi). Regular configurations with Dgeq6 can reach infinite radii, end with a cylinder of finite radius or possess two regular centres. The warp factors of configurations with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the centre. All of them are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models.