A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

Quantization of scalar field in cosmic spaces

Equations of scalar field are constructed by the method of embedding in conformally planar cosmic spaces of the general relativity theory (GRT). The equations are linear relative to the scalar field, which, on the one hand, enables one to regard the permutation function as a four-dimensional radially symmetric solution of the equation of the scalar field, and on the other hand, as a commutator of the wave solutions of the field; in this way the quantization laws are determined for the Fourier amplitudes of the solutions of the equations for the meson field. The wave solution of the scalar meson field is found in the conformally planar GRT space, and the permutation function is obtained as their commutator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 75–79, March, 1977.     

Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field

We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton?s constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martínez–Zanelli solution of Einstein?s equations with a negative cosmological constant coupled to conformal scalar field.     

Exact solutions of Einstein-conformal scalar equations

The massless scalar field which satisfies a conformally invariant equation is in some respects more interesting than the ordinary one. Unfortunately, few, if any, exact solutions of Einstein's equations for a conformal scalar stress-energy have appeared previously. Here we present a theorem by means of which one can generate two Einstein-conformal scalar solutions from a single Einstein-ordinary scalar solution (of which many are known). As an example we show how to obtain Weyl-like solutions with a conformal scalar field. We obtain and analyze in some detail two families of spherically symmetric static Einstein-conformal scalar solutions. We also exhibit a family of static spherically symmetric Einstein-Maxwell-conformal scalar solutions (parametrized by both electric and scalar charge), which have black-hole geometries but are not genuine black holes. Finally, we present all the Robertson-Walker cosmological models which contain both incoherent radiation and a homogeneous conformal scalar field. One class of these represents open universes which bounce and never pass through a singular state; they circumvent the “singularity theorems” by violating the energy condition.     

Zero-mass scalar and electrostatic fields with the central symmetry in the general relativity

All asymptotically flat space solutions of Einstein equations with energy-momentum tensor of electrostatic and zero-mass scalar static central symmetric fields as a source were found. There are five branches of general solution; only two of them are contained in previous Penney's solution. In a limit of pure electrostatic field and pure scalar field our solutions become identical with corresponding solutions known previously.     

Non-gravitating scalar field in the FRW background

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy–momentum tensor of the scalar field ϕ vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy–momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy–momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space–time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field χ.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Time-dependent solutions with localized energy of the Einstein system of equations and a nonlinear scalar field

A soliton-like time-dependent solution in the form of a running wave is derived of a self-consistent system of the gravitational field equations of Einstein and Born-Infeld type of equations of a nonlinear scalar field in a conformally flat metric. This solution is localized in space and possesses a localized energy. It is shown that both the gravitational field and the nonlinearity of the scalar field are essential to the presence of such a localized solution. In recent years various classical particle models have been widely discussed which are static or time-independent solutions of nonlinear equations with localization in space and which possess a finite field energy. In particular, soliton solutions [1], solutions in the form of eddies [2], and so on have been derived and investigated. All these solutions were treated in a flat space-time. It is of interest to derive the analogous particle-like solutions with the gravitational field taken into account; in particular it is of interest to investigate the roles of the gravitational field in connection with the formation of localized objects. These problems have been discussed in [3] in the static case. We will present below a soliton-like time-dependent solution in the form of a solitary running wave as an example of the inter-action of a Born-Infeld type of nonlinear scalar field and an Einstein gravitational field in a conformally flat metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–17, May, 1979.     

Cosmic Strings Coupled with a Massless Scalar Field

A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum-Einstein equations is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis, asymptotically flat, and free from the curvature singularities. The solution describes a stable, rotating cosmic string of infinite length interacting with gravitational and scalar waves.     

A plane symmetric solution of Einstein's field equations of general relativity containing zero-rest-mass scalar fields

An exact static solution of Einstein's field equations of general relativity in the presence of zero-rest-mass scalar fields has been obtained when both the metric tensor gijand the zero-rest-mass scalar field φexhibit plane symmetry in the sense of Taub [9]. Our solution generalizes the empty space-time solution with plane symmetry previously obtained by Taub to the situation when static zero-rest-mass scalar fields are present. The static plane symmetric solutoins of Einstein's field equations in the presence of massive scalar fields, and the difference between the massless and non-massless scalar fields are being investigated, and will be published separately later on. We also hope to discuss non-static plane symmetric solutions of Einstein's field equations in the presence of scalar fields in future.     

Propagation of Scalar Fields in a Plane Symmetric Spacetime

The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.     

EXACT SOLUTIONS OF CLASSICAL SCALAR FIELD EQUATIONS

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first-order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.     

Classical solutions of Yang-Mills and CP n−1 models with scalar fields

We present a study of classical solutions of the SU(2) Yang-Mills (YM) theory with a massless Higgs doublet, and of the CP ^n?1 model coupled to a scalar field. In both cases the scalar field tends to suppress instantons but not merons (this is a purely classical effect). In the YM theory a static Wu-Yang-like monopole solution with variable magnetic charge is found and its connection with the meron solution of this theory is discussed.     

Non-minimal kinetic coupling and Chaplygin gas cosmology

In the frame of the scalar field model with non-minimal kinetic coupling to gravity, we study the cosmological solutions of the Chaplygin gas model of dark energy. By appropriately restricting the potential, we found the scalar field, the potential and coupling giving rise to the Chaplygin gas solution. Extensions to the generalized and modified Chaplygin gas have been made.     

Causal green function in relativistic quantum mechanics

The causal Green function or Feynman propagator for the free-field Klein-Gordon equation and related singular functions, defined as distributions, are related to the causal time-boundary data. Probability densities and amplitudes are defined in terms of the solutions of the Klein-Gordon equation for a complex scalar field interacting with an electromagnetic field. The convergence of the perturbation expansion of the solution of the Klein-Gordon equation for a charged scalar particle in an external field is shown for well-behaved electromagnetic potentials. Other relativistic wave equations are discussed briefly.     

The Invariant-Related Unitary Transformation Method and the Evolution of Quantum Scalar Field in Robertson-Walker Flat spacetime

On the basis of the generalized invariant formulation, the invariant-related unitary transformation method is developed and used to study the evolution of a quantum scalar field in Robertson-Walker flat spacetime. We first solve the functional Schrödinger equation for a free scalar field and obtain the exact solutions, of which the 'ground-state' solution possesses isotropy and homogeneity automatically We then investigate the way of extending the method to treat the case in which there is a high-order perturbative self-in teraction.     

Cylindrically symmetric Brans-Dicke fields. I

A class of rigorous solutions for the Brans-Dicke scalar-tensor theory for Einstein-Rosen nonstatic cylindrically symmetric metric is obtained when only scalar field is present (vacuum solutions of Brans-Dicke theory). As the solutions of Brans-Dicke vacuum fields are conformal to either zero-mass scalar field or vacuum solutions of Einstein's gravitational theory, a set of solutions conformal to the above which correspond to zero-mass scalar field has also been obtained.     

Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement

The present paper deals with the electromagnetic (EM) scattering from a perfectly conductive, random surface by means of the stochastic functional approach and aims to study the backscattering enhancement associated with co-polarized and cross-polarized scattering. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener-Hermite functional of the homogeneous Gaussian random surface. To obtain more precise solutions than the previous works (Nakayama J et al 1981 Radio Sci. 16 831-53), we first establish the reciprocal theorem for vector Wiener kernels which describe the stochastic functional representation of the EM field and, using this, we derive the reciprocal relations for the co-polarized and cross-polarized scattering distribution relative to TE and TM polarizations of incident wave. Solutions for the vector Wiener kernels up to the second are obtained so precisely as to satisfy the reciprocal relations and are expressed in terms of generating matrices, so that complex EM scattering processes described by the vector Wiener kernels are given dear physical interpretations. Compact operator representations are introduced to reformulate the hierarchical kernel equations, the mass operator equation and higher-order kernel solutions. It is shown that the second vector Wiener kernel physically describes a 'dressed double-scattering' process, similar to the scalar theory (Ogura H and Takahashi N 1995 Waves Random Media 5 223-42), and that the 'dressed double scattering', which involves anomalous scattering in the intermediate scattering processes, creates the backscattering enhancement in both co- and cross-polarized scattering for both TE and TM wave incidence.     

Series solutions for a static scalar potential in a Salam-Sezgin Supergravitational hybrid braneworld

The static potential for a massless scalar field shares the essential features of the scalar gravitational mode in a tensorial perturbation analysis about the background solution. Using the fluxbrane construction of [8] we calculate the lowest order of the static potential of a massless scalar field on a thin brane using series solutions to the scalar field's Klein Gordon equation and we find that it has the same form as Newton's Law of Gravity. We claim our method will in general provide a quick and useful check that one may use to see if their model will recover Newton's Law to lowest order on the brane.     

Supersymmetry and classical solutions

We obtain classical solutions to the field equations of the massless supersymmetric Wess-Zumino model and to the field equations of the interacting SU(2) gauge supermultiplet. This is done by applying finite supersymmetry transformations to the known solutions of the scalar field equation with ?⁴ interaction and the Yang-Mills field equations. The relevance of supersymmetry to the solution of classical field equations involving anticommuting fermion fields is discussed.