No abstract

In this paper we examine the properties of U (1) gauged Q-balls in two models with different scalar field potentials. The obtained results demonstrate that in the general case U (1) gauged Q-balls possess properties, which differ considerably from those of Q-balls in the nongauged case with the same forms of the scalar field potential. In particular, it is shown that in some cases the charge of U (1) gauged Q-ball can be bounded from above, whereas it is not so for the corresponding nongauged Q-ball. Our conclusions are supported both by analytical considerations and numerical calculations.

Explicit solutions for extended objects of a Q-ball type were found analytically in a model describing complex scalar field with piecewise parabolic potential in (3+1)and (1+1)-dimensional space-times. Such a potential provides a variety of solutions which were thoroughly examined. It was shown that, depending on the values of the parameters of the model and according to the known stability criteria, there exist stable and unstable solutions. The classical stability of solutions in (1+1)-dimensional spacetime was examined in the linear approximation and it was shown explicitly that the spectrum of linear perturbations around some solutions contains exponentially growing modes while it is not so for other solutions. *

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.It is well known that in general case a four-dimensional pseudo-Riemannian manifold can be represented as a submanifold in a flat ten-dimensional space-time [1]. If the metric possesses additional symmetries the dimensionality of the ambient space-time may be smaller, for example, it is well known that the de Sitter space d S 4 can be represented as a hyperboloid in five-dimensional Minkowski space (for the first time explicit formulas for this embedding were presented in [2]). It is less known that the FRW (Friedmann-Robertson-Walker) space-times can also be embedded in five-dimensional Minkowski space (more generally, in pseudo-Euclidean spaces as we will show below). For the first time this fact was noticed almost 80 years ago in [3], where explicit formulas for the embeddings of the FRW universes were presented (see note D in [3]). In 1965 analogous formulas were presented in [4], where various embeddings of the solutions to equations of General Relativity in pseudo-Euclidean spaces were considered. Nevertheless, in spite of the recent activity in the field of embeddings of the four-dimensional General Relativity in five-dimensional flat or Ricci-flat space-times (see, for example, [5,6] and references therein), it looks as if