Field equations and vector order parameter in braneworld applications

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. Comparison with the commonly used scalar multiplet approach demonstrates the advantages of the vector order parameter.Comment: Text of the plenary report by B.E.Meierovich at the International Conference "Modern problems of gravitation, cosmology, and relativistic astrophysics", Moscow, June 27 -- July 3, 2010 (RUDN-10

Global Monopole in General Relativity

We consider the gravitational properties of a global monopole on the basis of the simplest Higgs scalar triplet model in general relativity. We begin with establishing some common features of hedgehog-type solutions with a regular center, independent of the choice of the symmetry-breaking potential. There are six types of qualitative behavior of the solutions; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. Thus, we show analytically that solutions with monotonically growing Higgs field and finite energy in the static region exist only in the interval $1<\gamma <3$, $\gamma$ being the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition on the Planck energy scale. In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with oscillating Higgs field. These families are parametrized by $n$, the number of knots of the Higgs field, and exist for $\gamma < \gamma_n = 6/[(2n+1) (n+2)]$; all such solutions possess a horizon and a singularity beyond it.Comment: 14 pages, 8 figure

Spontaneous Symmetry Breaking in General Relativity. Vector Order Parameter

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.Comment: 23 pages, 6 figure

Gravitating global monopoles in extra dimensions and the brane world concept

Multidimensional configurations with Minkowski external space-time and a spherical global monopole in extra dimensions are discussed in the context of the brane world concept. The monopole 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^i \phi^i. All possible kinds of globally regular configurations are singled out without specifying the shape of V(\phi). These variants are governed by the maximum value \phi_m of the scalar field, characterizing the energy scale of symmetry breaking. If \phi_m < \phi_cr (where \phi_cr is a critical value of \phi related to the multidimensional Planck scale), the monopole reaches infinite radii while in the ``strong field regime'', when \phi_m\geq \phi_cr, the monopole may end with a cylinder of finite radius or possess two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type 5D models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.Comment: 21 pages, 6 figures, latex, gc styl

Formation of bound states of electrons in spherically symmetric oscillations of plasma

We study spherically symmetric oscillations of electrons in plasma in the frame of classical electrodynamics. Firstly, we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Secondly, we consider both free and forced spherically symmetric oscillations of electrons. Finally, we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Huckel potential. We suggest that oscillating electrons can form bound states at the initial stages of the spherical plasma structure evolution. The possible applications of the obtained results for the theory of natural plasmoids are examined.Comment: 9 pages in LaTeX2e, no figures; paper was significantly modified, 2 new references added, some inessential mathematics was removed, many typos were corrected; final variant to be published in Physica Script

Pairing of charged particles in a quantum plasmoid

We study a quantum spherically symmetric object which is based on radial plasma oscillations. Such a plasmoid is supposed to exist in a dense plasma containing electrons, ions, and neutral particles. The method of creation and annihilation operators is applied to quantize the motion of charged particles in a self-consistent potential. We also study the effective interaction between oscillating particles owing to the exchange of a virtual acoustic wave, which is excited in the neutral component of plasma. It is shown that this interaction can be attractive and result in the formation of ion pairs. We discuss possible applications of this phenomenon in astrophysical and terrestrial plasmas.Comment: 17 pages, no figures, two columns, LaTeX2e; paper was significantly revised; title was changed; 16 new references were included; the discussion on ion-acoustic waves was added to Sec. 2; Secs. 3 and 4 were shortened; a more detailed discussion was added to Sec. 7; accepted for publication to J.Phys.

Landau damping and anomalous skin effect in low-pressure gas discharges: Self-consistent treatment of collisionless heating

In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is reported. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. This system was applied to the calculation of collisionless heating in capacitively and inductively coupled plasmas. In particular, the importance of accounting for the nonuniform plasma density profile for computing the current density profile and the EEDF is demonstrated. The enhancement of collisionless heating due to the bounce resonance between the electron motion in the potential well and the external radio-frequency electric field is investigated. It is shown that a nonlinear and self-consistent treatment is necessary for the correct description of collisionless heating