On the evolution equations for a self-gravitating charged scalar field

We consider a complex scalar field minimally coupled to gravity and to a U(1) gauge symmetry and we construct of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Klein-Gordon system. Our analysis is based on a $1+3$ tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations, implied by the Bianchi identity, we introduce a tensor of rank 3 corresponding to the covariant derivative of the Faraday tensor, and two tensors of rank 2 for the covariant derivative of the vector potential and the scalar field.     

The problem of scalar field theory in curved space-time

It is demonstrated that (1) there exist infiniteG ₁ that satisfy Lichnerowicz's conditions (L conditions) in a globally hyperbolic manifold; and, (2) there is noG ₁ in an expanding universe that would satisfy those conditions and that would behave as the ordinary ₁ of flat space whenx x. The author thinks that these results present a serious problem for finding a semiclassical theory of scalar field in curved space-time.     

Five-dimensional geometric electrovacuum problem with a geometric scalar field

A generalized geometric Reissner–Nordstrom problem taking into account a geometric scalar field G ₄₄ (x) is treated in the context of the five-dimensional geometric theory of gravitation and electromagnetism. A general solution is obtained for the corresponding five-dimensional Einstein vacuum equations. The essential contribution of the geometric scalar field, which can give rise to wormholes, is shown.     

Localization of scalar fields on self-gravitating thick branes

The model of a domain wall (“thick” brane) in noncompact five-dimensional spacetime is considered with geometries of AdS ₅ type generated by self-interacting scalar matter. The scalar matter is composed of two fields with O(2) symmetric self interaction. One of them is mixed with gravity scalar modes and plays role of the brane formation mode (due to a kink background) and another one is of a Higgs-field type. The interplay between soft breaking of O(2) symmetry and gravity influence is thoroughly investigated around the critical point of spontaneous t symmetry breaking when the v.e.v. of the Higgs-type scalar field occurs. The possibility of (quasi)localization of scalar modes on such thick branes is examined.     

Bose-Einstein condensation in a static scalar field from the standpoint of the Goursat problem

The Goursat problem, developed by the present authors in previous papers [Ukr. Fiz. Zh. (Russ. Ed.) 27, 1602 (1982); Differentsial’nye Uravneniya 20, 302 (1984); J. Math. Phys. 33, 233 (1996)], is used to study the energy spectrum of a scalar relativistic particle in a static axisymmetric external scalar field of an attractive nature. This is obviously a model. It is shown that the problem formulated in this way has no unstable solutions, i.e., solutions increasing with time, in contrast to the Cauchy problem, where such solutions appear when the square of the particle frequency (energy) vanishes (in other words, in a Bose-Einstein condensation) Zh. éksp. Teor. Fiz. 112, 1167–1175 (October 1997)     

Anisotropy of a relict scalar field

It is shown that anisotropy of relict radiation can be caused by anisotropy of a relict scalar field, and large-scale structures of the relict scalar field can lead to large-scale structures of baryon matter. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–11, January, 2009.     

Decay of a Yang-Mills field coupled to a scalar field

Consider a gauge fieldF and a scalar field with a self-couplingV() as well as the standard coupling betweenF and . If 02V()·V(), there are no classical lumps. IfV()=||⁴ the system is conformally invariant and all the energy radiates out along the light cone.Research supported in part by NSF grants MCS 77-01340 and MCS 78-03567     

Colored scalar in a chromomagnetic field

The motion of colored scalar particles in a constant color magnetic field is considered. The Klein-Gordon equation is solved in this background and the energy spectrum is quantized by boundary conditions. The unitary transformation diagonalizing this equation and the states with definite energy are found.     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

The effect of a non-minimally coupled scalar field upon classical thermodynamics

It is known that a scalar field that is non-minimally coupled to the geometry implies a varying gravitational “constant” G_eff, and hence a violation of the continuity equations, $\text{T}\text{?}{}^{\mathrm{ik}}{}_{\mathrm{;k}}\text{≠ 0}$, where $\text{T}\text{?}{}_{\mathrm{ij}}$ is the uncorrected energy-momentum tensor. This in turn upsets classical thermodynamics. 3he simplest resolution of this difficulty is to multiply all energetic quantities by $\text{G}{}_{\mathrm{<mtext>eff</mtext>}}\text{G}{}_{\mathrm{<mtext>N</mtext>}}$, where G_N is the newtonian gravitational constant. This modified thermodynamics is applied to the scalar-field version of the cosmological model of Zee, for which it is shown to cause restoration of the symmetry above some critical temperature T_c close to the Planck temperature. We also illustrate how the second law of thermodynamics is always obeyed, correcting a recent discussion by Davies.     

The Brans-Dicke scalar field in Einstein-Cartan theory

In the framework of Einstein-Cartan (EC) theory, the Brans-Dicke (BD) theory is considered and it is found that a scalar field nonminimally coupled to the gravitational field gives rise to torsion, even though the scalar field has zero spin. The metric equations stay the same if the coupling constant is rescaled, but the equations of motion of a test particle, derived from the conservation equations, differ from those of the usual BD theory without torsion. The gravitational red-shift value differs considerably from the usual prediction of general theory of relativity (GTR), and rules out the possibility of a torsion version of BD theory for<6.     

Passive scalar in a large-scale velocity field

We consider advection of a passive scalar θ(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model all PDF’s (probability distribution functions) for the single-point statistics of θ and for the passive scalar difference θ(r ₁)−θ(r ₂) (for separations r ₁−r ₂ lying in the convective interval) are found. Zh. éksp. Teor. Fiz. 115, 920–939 (March 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.