Scalar Fields in Multidimensional Gravity. No-Hair and Other No-Go Theorems

Global properties of static, spherically symmetric configurations with scalar fields of sigma-model type with arbitrary potentials are studied in D dimensions, including models where the space-time contains multiple internal factor spaces. The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and the potential V includes a contribution from their curvatures. The following results generalize those known in four dimensions: (A) a no-hair theorem on the nonexistence, in case V 0, of asymptotically flat black holes with varying scalar fields or moduli fields outside the event horizon; (B) nonexistence of particlelike solutions in field models with V 0; (C) nonexistence of wormhole solutions under very general conditions; (D) a restriction on possible global causal structures (represented by Carter-Penrose diagrams). The list of structures in all models under consideration is the same as is known for vacuum with a cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild – de Sitter, and horizons which bound a static region are always simple. The results are applicable to various Kaluza-Klein, supergravity and stringy models with multiple dilaton and moduli fields.     

Integrable multicomponent perfect fluid multidimensional cosmology. I

Multidimensional cosmological models with a space-time consisting ofn (n 2) Einstein spaces are investigated for a special class of multicomponent perfect fluid as a matter source. The dynamical behaviour of the universe is described. In the case of static internal spaces the external space evolves like a Friedmann universe with changing effective equation of state. Some of the models considered are integrable and classical as well as quantum solutions are found. Some of them represent wormholes. Quantum wormholes have a discrete spectrum.     

Higher Dimensional Cosmological Model With Gravitational and Cosmological "Constants"

In this paper we have considered a cosmological model representing a flat viscous universe with variable G and in the context of higher dimensional spacetime. It has been observed that in this model the particle horizon exists and the cosmological term varies as inverse square of time. The deceleration parameter and temperature are well within the observational limits. The model indicates matter and entropy generation in the early stages of the universe. Further, it is shown that our model generates all models obtained by Arbab and Singh et al. in four-dimensional space-time.     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

Self-tuning and de Sitter brane intersections in 6-dimensional brane models

We study the self-tuning of general brane junctions and brane networks on 6-dimensional space-time. For general brane junctions, there may exist one fine-tuning among the brane tensions. For the brane networks, similar to the 5-dimensional self-tuning brane models, the brane tensions can be set arbitrarily and there exists a singularity for the metric and bulk scalar. If we want to regularize the singularity, we will introduce fine-tuning among the brane tensions. In addition, because the 4-dimensional cosmological constant we observe may be positive and very small, we discuss the brane network with de Sitter brane intersections by introducing a bulk scalar. Received: 8 November 2001 / Published online: 20 November 2002 RID="a" ID="a" Present address: Division of High Energy Physics, Argonne National Laboratory, Argonne IL 60439, USA RID="b" ID="b" Present address: School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA. E-mail: tli@sns.ias.edu     

Gravitational and quantum effects in rotating cosmological models

Specific effects of the dynamics of (spinor and scalar) wave fields are considered in rotating uniform Gödel-type cosmological models. It is shown that the gravitational interaction of the spinor field can be reduced to the interaction between its pseudovector current and the angular velocity of space-time rotation and is similar to its interaction with the pseudotrace of the space-time twisting. The mean values of energy-momentum tensor of the quantized scalar field in vacuum are calculated in rotating cosmological models and the difference between these values and their mean counterparts in vacuum is determined for Friedman's nonrotating cosmological models.State Education Institute, Yaroslavl'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–38, June, 1992.     

Cosmological aspects of the gravitational interaction of a scalar field in the affine-metric theory of gravitation

The gravitational interaction of a scalar field, with allowance for the possible influence of the torsional and nonmetric nature of space-time, is investigated within the framework of the affine-metric theory of gravitation. The equations of the theory are derived from the variational principle. It is shown that in an affine-metric space, the combined Lagrangian of the gravitational and scalar fields with conformal coupling is reduced to the Lagrangian of the system of gravitational and axion fields in the general theory of relativity. All of the exact general solutions of the consistent system of equations of gravitational and scalar (massless) fields in the affine-metric space under consideration are obtained for all types of homogeneous Friedmann cosmological models, with the initial singularity being removed from some of them. Homogeneous, anisotropic cosmological models, for which all of the exact general solutions are also obtained, are investigated. Some of these models are nonsingular, and the effect of isotropization due to the torsional and nonmetric nature of space-time occurs for many of them. K. D. Ushinskii State Pedagogical University, Yaroslavl’. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–50, May, 1998.     

Bianchi VI0 models in N=2, D=5 supergravity

We investigate Bianchi VI₀ cosmological models containing two interacting scalar fields. These models are derived from a dimensional reduction of theN=2,D=5 supergravity theory. Exact solutions are found and the existence of singularities for them is considered.     

The Inflationary Solutions with O(2,2) Duality Symmetry in String Cosmologies

The low energy duality string model is investicated in time-dependent metric, torsion, dilaton background fields and potential fields, the inflationary solutions for string cosmologies are obtained when the space-time dimension is D = 3. It is found that the new cosmological solutions can be generated through O(d, d) duality transformations.     

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models; among them spherically reduced theories and the string inspired dilaton black hole. We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way, asymptotic states, tree-level vertices and the tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the string inspired dilation black hole all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.Received: 7 August 2002, Revised: 2 June 2003, Published online: 11 July 2003D.V. Vassilevich: On leave from V. Fock Institute of Physics, St. Petersburg University, 198904 St. Petersburg, Russia     

Stringy differential geometry for double field theory, beyond Riemann

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D, D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. We comment that the notion of cosmological constant naturally changes.     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

Bianchi type-I,V and VIo models in modified generalized scalar-tensor theory

In modified generalized scalar-tensor (GST) theory, the cosmological term Λ is a function of the scalar field ϕ and its derivatives . We obtain exact solutions of the field equations in Bianchi Type-I, V and VIo space-times. The evolution of the scale factor, the scalar field and the cosmological term has been discussed. The Bianchi Type-I model has been discussed in detail. Further, Bianchi Type-V and VIo models can be studied on the lines similar to Bianchi Type-I model.      

Phantom divide crossing with general non-minimal kinetic coupling

We propose a model of dark energy consists of a single scalar field with a general non-minimal kinetic couplings to itself and to the curvature. We study the cosmological dynamics of the equation of state in this setup. The coupling terms have the form \({\xi_{1} Rf(\phi)\partial_{\mu}\phi\partial^{\mu}\phi}\) and \({\xi_{2}R_{\mu\nu}f(\phi)\partial^{\mu}\phi\partial^{\nu}\phi}\) where ξ ₁ and ξ ₂ are coupling parameters and their dimensions depend on the type of function \({f(\phi)}\). We obtain the conditions required for phantom divide crossing and show numerically that a cosmological model with general non-minimal derivative coupling to the scalar and Ricci curvatures can realize such a crossing.     

Cosmological models without singularities

A previously studied theory of gravitation in flat space-time [Petry, W. (1981).Gen. Rel. Grav. 13, 865] is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models we get at the beginning of the universe—in contrast to Einstein's theory—very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal zero and cosmological constant 0.     

The unified field theory,combining Kaluza's five-dimensional and Weyl's conformal theories

A version of the five-dimensional unified theory of gravitation, electromagnetism, and scalar field is developed. It is shown that in this theory the main features of Kaluza's five-dimensional theory and the Weyl one, based on non-Riemannian geometry and on conformal mapping, are combined. Some reasons are pointed out for choosing the physical 4-metric to be conformal (with the factor ²=–G ₅₅) to the 4-metric obtained by 1+4 splitting of the initial five-dimensional manifold. It is shown that the electrical charge and current appear in the geometrical theory if the condition of cylindrical symmetry in the fifth coordinate is substituted by the condition of quasicylindrical symmetry (i.e., the physical 4-metric and the vector potential of electromagnetic field remain independent of the fifth coordinate, while the scalar field depends on it). Two kinds of the most important exact solutions of the 15 field equations are considered. They are (1) static spherically symmetrical solutions and (2) homogeneous isotropic cosmological models.     

Special conformal symmetries in general relativity

A geometrical discussion of special conformal vector fields in space-time is given. In particular, it is shown that if such a vector field is admitted, it is unique up to a constant scaling and the addition of a homothetic or a Killing vector field. In the case when the gradient of the conformal scalar associated with is non-null it is shown that other homothetic and affine symmetries are necessarily admitted by the space-time, that an intrinsic family of 2-dimensional flat submanifolds is determined in the space-time, that is, in general, hypersurface orthogonal and that the space-time, if non-flat, is necessarily (geodesically) incomplete. Other geometrical features of such space-times are also considered.