Showing papers in "Gravitation & Cosmology in 2001"

The Fundamental supersymmetry challenge remains

Abstract: In the following, we will review the fundamental problem that prevents a complete understanding of a theory of supersymmetrical field representations and describe its possible relation to a similar problem facing superstring/M-theory.

Spherically symmetric scalar vacuum: No go theorems, black holes and solitons

Abstract: We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and all horizons are simple. In particular, these theories do not admit regular black holes with any asymptotics. Some special features of (2+1)D gravity are revealed. We give examples of two types of asymptotically flat configurations with positive mass in GR, admitted by the above theorems: (i) a black hole with nontrivial ``scalar hair'' and (ii) a particlelike solution with a regular centre; in both cases, the potential $V$ must be at least partly negative. We also discuss the global effects of conformal mappings that connect different theories. Such effects are illustrated for solutions with a conformal scalar field in GR.

BPS Lumps and Their Intersections in N = 2 SUSY Nonlinear Sigma Models

Abstract: BPS lumps in ${\\cal N}=2$ SUSY nonlinear sigma models on hyper-\\kahler manifolds in four dimensions are studied. We present new lump solutions with various kinds of topological charges. New BPS equations and a new BPS bound, expressed by the three complex structures on hyper-\\kahler manifolds, are found. We show that any states satisfying these BPS equations preserve 1/8 (1/4) SUSY of ${\\cal N}=2$ SUSY nonlinear sigma models with (without) a potential term. These BPS states include non-parallel multi-(Q-)lumps.

Noncommutative N=2 supersymmetric theories in harmonic superspace

Abstract: We discuss a formulation of harmonic superspace approach for noncommuative N=2 supersymmetric field theories paying main attention on new features arising because of noncommutativity. We begin with the known notions of the harmonic superfield models and results obtained and consider how these notions and results are modified in the noncommutative case. The actions of basic N=2 models, like hypermultiplet and N=2 vector multiplet, are given in terms of unconstrained off-shell superfields on noncommutative harmonic superspace. We calculate the low-energy contributions to the effective actions of these models. The background field method in noncommutative harmonic superspace is developed and it is applied to study the 1-loop effective action in general noncommutative N=2 model and N=4 SYM theory.

Equations of Motion in Kaluza-Klein Gravity Revisited

Abstract: We discuss the equations of motion of test particles for a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric tensor of the five-dimensional manifold is allowed to depend on the fifth coordinate. This is the usual working scenario in brane-world, induced-matter theory and other Kaluza-Klein theories with large extra dimensions. We present a new version for the fully covariant splitting of the 5D equations. We show how to change the usual definition of various physical quantities in order to make physics in 4D invariant under transformations in 5D. These include the redefinition of the electromagnetic tensor, force and Christoffel symbols. With our definitions, each of the force terms in the equation of motion is gauge invariant and orthogonal to the four-velocity of the particle. The "hidden" parameter associated with the rate of motion along the extra dimension is identified with the electric charge, regardless of whether there is an electromagnetic field or not. In addition, for charged particles, the charge-to-mass ratio should vary. Therefore, the motion of a charged particle should differ from the motion of a neutral particle, with the same initial mass and energy, even in the absence of electromagnetic field. These predictions have important implications and could in principle be experimentally detected.

Status of a self - bound equations of state and analytic solutions in general relativity

Abstract: We have obtained a criterion for spherically symmetric and static structures under hydrostatic equilibrium in general relativity (GR), which states that for a given value of σ ≡ (P0/E0) ≡ the ratio of central pressure to central energydensity], the compaction parameter u ≡ (M/a) , where M is the total mass and a is the radius of the configuration] or the surface redshift of any regular configuration cannot exceed that of the corresponding homogeneous density sphere, that is, u ≤ uh , where uh is the compaction parameter of the homogeneous density sphere. By examining various exact solutions and equations of state available in the literature, we find that this criterion is fulfilled only by those configurations in which the surface density vanishes alongwith the pressure (meaning thereby that the pressure, energy density, metric parameters and their first derivatives are continuous on the surface). On the other hand, configurations having a finite density on the surface (that is, the self-bound structures) do not fulfill this criterion. This criterion puts a severe restriction on the static structures based upon the general relativistic field equations and consequently on the upper limit of mass, surface and central redshift and other physical parameters of spherically symmetric and static configurations.

Inflation with oscillations

Abstract: In this paper we investigate the general features of "Oscillatory Inflation". In adiabatic approximation, we derive a general formula for the number of e-foldings $\tilde{N}$ which reduces to the standard expression in case of the slow role approximation and leads to the Damour-Mukhanov type expression for the slowly varying adiabatic index. We apply our result to the logarithmic potential and arrive at a simple and elegant formula for the number of e-foldings. We evolve the field equations numerically and observe a remarkable agreement with the analytical result.

Yang-Mills theory as a quantum gravity with 'aether'

Abstract: Quantum Yang–Mills theory can be rewritten in terms of gauge-invariant variables: it has the form of the so-called BF gravity, with an additional ‘aether’ term. The BF gravity based on the gauge group SU(N) is actually a theory of high spin fields (up to J = N ) with high local symmetry mixing up fields with different spins — as in supergravity but without fermions. As N → ∞ , one gets a theory with an infinite tower of spins related by local symmetry, similar to what one has in string theory. We thus outline a way of deriving a string theory from the local Yang–Mills theory in the large N limit.

Symmetry, singularities and intregrability in complex dynamics VII: Integrability Properties of FRW-Scalar Cosmologies

Abstract: This paper considers some physically interesting cosmological dynamicalsystems in the FRW-scalarfield category which are examined for integra-bility according to the criterion of Painlev´e. In the literature these systemshave been examined from the point of view of dynamical systems and theresults from the two disparate methods of analysis are compared. Thisallows some more general comments to be made on the use of the Painlev´emethod in covariant systems. 1 Introduction This is the seventh in a series of papers [1, 2, 3, 4, 5, 6] devoted to variousaspects of the three mathematically disparate topics of symmetry, singularitiesand integrability of dynamical systems. It is the purpose of the series to cementthe concepts into a greater obvious unity whereby they are recognised as dif-ferent aspects of the central properties of dynamical systems which distinguishintegrable systems from nonintegrable systems.The plan of the present paper is as follows. In §2 we present a brief resum´eof the analysis of Painlev´e with particular reference to some of the subtletiesrequired to deal with systems which do not fit into the neat scheme of the

Cylindrically Symmetric Solitons with Nonlinear Self-Gravitating Scalar Fields

Abstract: Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions. Some non-existence theorems are proved, in particular, theorems asserting (i) the absence of black-hole and wormhole-like cylindrically symmetric solutions for any static scalar fields minimally coupled to gravity and (ii) the absence of solutions with a regular axis for scalar fields with the Lagrangian $L=F(I)$, $I=\phi^\alpha \phi_\alpha$, for any function $F(I)$ possessing a correct weak field limit. Exact solutions for scalar fields with an arbitrary potential function $V(\phi)$ are obtained by quadratures and are expressed in a parametric form in a few ways, where the parameter may be either the coordinate $x$, or the $\phi$ field, or one of the metric coefficients. Soliton-like solutions are shown to exist only with $V(\phi)$ having a variable sign. Some explicit examples of solutions (including a soliton-like one) and their flat-space limit are discussed.}

On the way to brane new world

Abstract: In this report we consider brane-world universe (New Brane World) where an arbitrary large $N$ quantum CFT exists on the domain wall. This corresponds to implementing of Randall-Sundrum compactification within the context of AdS/CFT correspondence. Using anomaly induced effective action for domain wall CFT, the possibility of self-consistent quantum creation of 4d de Sitter wall universe (inflation) is demonstrated. In case of maximally SUSY Yang-Mills theory the exact correspondence with radius and effective tension found by Hawking-Hertog-Reall is obtained. We also discuss the bosonic sector of 5d gauged supergravity with single scalar and taking the boundary action as predicted by supersymmetry and discuss the possibility to supersymmetrize dilatonic New Brane World. It is demonstrated that for a number of superpotentials the flat SUSY dilatonic brane-world (with dynamically induced brane dilaton) or quantum-induced de Sitter dilatonic brane-world (not Anti-de Sitter one) where SUSY is broken by the quantum effects occurs. The analysis of graviton perturbations indicates that gravity is localized on such branes. New Brane World is useful in the study of FRW dynamics and cosmological entropy bounds. Brane stress tensor is induced by quantum effects of dual CFT and brane crosses the horizon of AdS black hole. The similarity between CFT entropy at the horizon and FRW equations is extended on the quantum level. This suggests the way to understand cosmological entropy bounds in quantum gravity.

Field Transformation in the Extended Space Model: Prediction and Experimental Test

Abstract: A run of preliminary experiments was carried out to check the prediction of possible gravitational field generation process arising by stopping of charged massive particles in a substance predicted by the recently developed Extended Space Model (ESM) [1, 3]. ESM is a model of the extended (1+4)-dimensional space G(T ; ~ X, S) with the interval S as the fifth coordinate. Certainly, these five coordinates satisfy the relation (ct) −x− y− z− s = 0. In addition to the Lorentz transformations (T ; ~ X) in (1+3)-dimensional Minkowski space, in ESM there exist two other transformations in the planes (T ;S) and ( ~ X ;S). They convert massive particles into massless ones and vice versa. We also considered the energy-momentum-mass (1+4)D space G(E; ~ P ,M) = (E/c; ~p,mc) which is conjugated to the time-coordinates-interval (t;x, y, z, s) (1+4)D space, and thus a mass m in 5D space G(E; ~ P ,M) corresponds to the interval s in 5D space G(T ; ~ X, S). The coordinates in (1+4)D space G(E; ~ P ,M) satisfy the relation E − c2p2x − c 2p2y − c 2p2z −m c = 0. Note that this model differs from the analogous 5D theory developed in [6], in which mass is considered as the fifth coordinate in 5D time-coordinate-mass (matter) space. In such an approach it is impossible to build energy-momentum tensor due to mixing of mass coordinate with time and spatial coordinates. In the proposed ESM the well-known energy-momentum 4-vector P (1 + 3) = (E/c; px, py, pz) = (E/c; ~p) in Minkowski space M(T ; ~ X) is transformed to the 5vector P (1 + 4) = (E/c; ~p,mc) in the extended space G(T ; ~ X, S) and becomes null for 5-vectors of a massive particle at rest (mc;~0,mc) as well as for a massless particle (hω/c; hω~k/c, 0) (here ~k is the unit vector in the particle propagation direction). The basic predictions of general relativity can also be obtained in ESM. For instance, the following gravitational effects have been considered in [5]: the planet escape velocity, starlight redshift and deflection, and re-

D-dimensional integrable 2-component viscous cosmology

Abstract: A D -dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing bothsh ear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are chosen in some special form of metric dependence of the shear and bulk viscosity coefficients. The equations of motion are integrated, and the dynamical properties of exact solutions are studied. It is shown that the 2-component model, where the x-fluid plays the role of a quintessence and the viscous fluid is used as cold dark matter, is free from the cosmic coincidence problem.

Thick brane world model from perfect fluid

Abstract: A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model is generalized to the case of a chain of Ricci-flat internal spaces when the matter source is an anisotropic perfect fluid. The "horizontal" part of potential is obtained in the Newtonian approximation. In the multitemporal case (with a Lambda-term) a set of equations for potentials is presented.

Some cosmological consequences of the five-dimensional projective unified field theory

Abstract: The classical observational cosmological tests (Hubble diagram, count of sources, etc.) are considered for a homogeneous and isotropic model of the Universe in the framework of the five-dimensional Projective Unified Field Theory in which gravitation is described by both space-time curvature and some hypothetical scalar field (sigma-field). It is shown that the presence of the sigma-field can essentially affect conclusions obtained from the cosmological tests. The surface brightness-redshift relation can be used as a critical test for sigma-field effects. It seems reasonable to say that the available experimental data testify that the sigma-field decreases with time. It is concluded that the spatial curvature is positive or negative depending on whether the mass density is larger or smaller than some critical parameter which is smaller than the critical density and can even take negative values. It is shown that the increase in the number of the observational cosmological parameters as compared to the standard Friedmann model can essentially facilitate coordination of the existing observational data.

Can the hierarchy problem be solved by finite-temperature massive fermions in the randall-sundrum model?

Abstract: Quantum effects of bulk matter, in the form of massive fermions, are considered in the Randall-Sundrum AdS5 brane world at finite temperatures. The thermodynamic energy (modulus potential) is calculated in the limiting case when the temperature is low, and is shown to possess a minimum, thus suggesting a new dynamical mechanism for stabilizing the brane world. Moreover, these quantum effects may solve the hierarchy scale problem, at quite low temperatures. The present note reviews essentially the fermion-related part of the recent article by I. Brevik, K. A. Milton, S. Nojiri, and S. D. Odintsov, Nucl. Phys. B 599, 305 (2001).

Extended quadruple-kerr metric

Abstract: An exact axisymmetric solution of Einstein’s equations describing the exterior gravitational field of four aligned Kerr particles is considered. The balance conditions are derived in the case of particles possessing an additional reflection symmetry with respect to the equatorial plane. A numerical analysis of these conditions suggests the non-existence of physically relevant equilibrium configurations in such systems.