Nonlinear perturbations of the Kaluza-Klein monopole

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of Bogomol'nyi-Prasad-Sommerfield states in M or string theory is briefly discussed.     

Kaluza-Klein monopoles and gauged sigma-models

We propose an effective action for the eleven-dimensional (bosonic) Kaluza-Klein monopole solution. The construction of the action requires that the background fields admit an Abelian isometry group. The corresponding sigma-model is gauged with respect to this isometry. The gauged sigma-model is the source for the monopole solution. A direct (double) dimensional reduction of the action leads to the effective action of a 10-dimensional D-6-brane (IIA Kaluza-Klein monopole). We also show that the effective action of the 10-dimensional heterotic Kaluza-Klein monopole (which is a truncation of the IIA monopole action) is T-dual to the effective action of the solitonic 5-brane. We briefly discuss the kappa-symmetric extension of our proposal and the possible role of gauged sigma-models in connection with the conjectured M-theory 9-brane.     

Dual doubled geometry

We probe doubled geometry with dual fundamental branes, i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundamental branes. This dual wrapping rule can be understood by the presence of Kaluza-Klein monopoles. Extending our analysis to supersymmetric solitonic branes with less than or equal to two transverse directions we show that such solitons are precisely obtained by applying the same dual wrapping rule to these cases as well. This extended wrapping rule cannot be explained by the standard Kaluza-Klein monopole alone. Instead, it suggests the existence of a class of generalized Kaluza-Klein monopoles in ten-dimensional string theory.     

The motion of charged particles in Kaluza-Klein space-time

The equations of motion for charged particles are derived from the geodesic hypothesis in the five-dimensional Kaluza-Klein theory. It is shown that even within this purely classical framework the theory does not describe low mass charged particles, and that in the background of a Kaluza-Klein monopole, the long range scalr field has striking observable consequences for electron motion, even at very large distances.     

String dynamics near a black hole

The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the geodesic equations are obtained using the world sheet velocity of light as an expansion parameter. For a string falling into a magnetically charged black hole, it is shown that the compact dimension decreases with the world-sheet coordinate τ.     

Cosmological production of Kaluza-Klein monopoles

The cosmological production of Kaluza-Klein monopoles is discussed. The present monopole-to-entropy ratio is calculated in some simple models with the conclusion that this ratio is unacceptably large unless additional mechanisms for entropy production or monopole annihilation are present.     

Defect branes

We discuss some general properties of “defect branes”, i.e. branes of co-dimension two, in (toroidally compactified) IIA/IIB string theory. In particular, we give a full classification of the supersymmetric defect branes in dimensions 3?D?10 as well as their higher-dimensional string and M-theory origin as branes and a set of “generalized” Kaluza-Klein monopoles. We point out a relation between the generalized Kaluza-Klein monopole solutions and a particular type of mixed-symmetry tensors. These mixed-symmetry tensors can be defined at the linearized level as duals of the supergravity potentials that describe propagating degrees of freedom. It is noted that the number of supersymmetric defect branes is always twice the number of corresponding central charges in the supersymmetry algebra.     

Fermions and the Kaluza-Klein monopole

This paper investigates the behavior of light charged matter in the presence of the recently constructed Kaluza-Klein monopole, starting with a mechanism for obtaining such matter in the first place. For scalars the separation of variables is identical to that for the ordinary Dirac monopole, but the geometrical picture sheds some light on the strange quantum numbers of the resulting states. Fer fermions there is a new repulsive potential, even in the lowest partial wave. This renders the hamiltonian self-adjoint without any family of extensions, in contrast to the Dirac pole. Consideration of quantum effects on long-distance physics, however, modifies the basic monopole solution and restores the usual fermion physics.     

O(4,2) dynamical symmetry of the Kaluza-Klein monopole

The o(4)/o(3,1) dynamical symmetry of the Gross-Perry-Sorkin monopole in five-dimensional Kaluza-Klein theory (which also describes the asymptotic scattering of BPS monopoles) is extended, in analogy to the Kepler problem, to the conformal algebra of o(4,2).     

Comment on the nonsymmetric Kaluza-Klein theory with material sources

In this paper we consider some new numerical predictions of the nonsymmetric Kaluza-Klein theory with non-zero material sources. We prove that they do not contradict any experimental data in the solar system and on the surface of a neutron star. We deal also with equations for geodesics and spin sources in the nonsymmetric Kaluza-Klein theory. We discuss some details from the nonsymmetric Kaluza-Klein theory.     

Spectroscopy of the Rotating Kaluza-Klein Spacetime via Revisited Adiabatic Invariant Quantity

In this paper, we have investigated the spectroscopy of the rotating Kaluza-Klein spacetime by applying Bohr–Sommerfeld quantization rule and the first law of thermodynamics. we derived the expression of the adiabatic invariant quantity in the dragged–Painlevé coordinate system. Then, via revisited adiabatic invariant quantity, we derive the area and entropy spectra of the spacetime. We obtained the area spectrum of the Kaluza-Klein spacetime is \({\Delta } A=8\pi {l_{P}^{2}}\), and the entropy spectrum is ΔS = 2π. This result is consistent with the Bekenstein’s original result, which imply the entropy and horizon area are discrete and equidistant for the spacetime.     

采用分布式球形阵列的球谐波域声场分离方法

为从测得的混合声场信号中提取出需要的目标声场,提出一种基于分布式球形传声器阵列的声场分离方法。该方法依据声场的球谐波分解,利用阵列各传声器采集到的声场声压信号,获得目标声场与干扰声场的球谐波展开系数,进而估计目标声场。该方法利用声场以不同中心展开的球谐波系数之间的变换关系,直接建立传声器测量声压信号与整体坐标系下声场展开系数的方程,与传统的分布式球形阵列声场分离方法,即先求解局部坐标系下声场展开系数,再变换为整体展开系数的方法,进行比较。分别通过数值仿真和实验说明了提出方法的有效性。结果表明:该方法能够从混合声场中较准确地估计出目标声场,并且在干扰声场能量增大时,保持了较小的声场估计误差,相比于传统方法误差增加更少。     

Effect of particle production on the evolution of a low entropy universe

The oscillation of a classical field causes particle production, which then influences the evolution of the early universe. We examine this problem by solving a coupled system of Einstein-Boltzmann equations. In particular, particle production, caused by a damped oscillation of the extra space just prior to the compactification in vacuum Kaluza-Klein cosmology, leads to a period governed by an expansion law, with scale factor ∞ time.     

Kaluza-Klein unification in the poincaré gauge theory of gravitation

We show that we can unify the gravitational and internal gauge interactions in a high dimensional Riemann-Cartan spacetime in the spirit of Kaluza-Klein, if we identify some of the connection coefficients as Yang-Mills potentials and if the dynamics of the spacetime is governed by the Poincaré gauge theory of gravitation whose lagrangian contains curvature and torsion squared.     

The covariant form of the Klein-Kramers equation and the associated moment equations

We provide a covariant, coordinate-free formulation of the many-dimensional Klein-Kramers equation for the phase space distribution of a Brownian particle. We construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system, which involve covariant tensorial Hermite polynomials. The Klein-Kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system. Truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of Grad's thirteen-moment equations. As an application we give the explicit form of these equations for spherically symmetric, stationary solutions in spherical coordinates. We briefly comment on possible extensions of our treatment to slightly more complicated cases.     

Instability of a scalar field in a geometry with anisotropic inflation

It is shown that ever-increasing long-wave fluctuations are generated for a light scalar field in metrics which have exponential expansion (inflation) on some coordinates (including Kaluza-Klein models). This result generalizes the well-known result for the de Sitter metric, and may be important in Kaluza-Klein models with dynamical reduction and for the pre-inflationary spacetime foam.     

Four-dimensional supersymmetric black holes of type IIA superstring

We systematically construct a large class of four-dimensional supersymmetric black hole solutions of toroidally compactified type IIA superstring theory by explicitly solving the Killing spinor equations. They correspond to orthogonally intersecting configurations in ten dimensions. With the Kaluza-Klein monopole, they are parameterized by four charges and preserve of the N = 8 supersymmetry. We found a simple map to associate each charge with the corresponding Killing spinor constraints. The embedding of the N = 4 supersymmetry of a toroidally compactified heterotic string into the N = 8 supersymmetry of the IIA superstring was explicitly shown. We also found explicitly the configurations with only Ramond-Ramond charges, and those with both Neveu-Schwarz Neveu-Schwarz charges and Ramond-Ramond charges, including the dilaton and the internal metrics. The T-dual of these configurations were shown to satisfy the Killing spinor equations as well.     

Plane-wave,coordinate-space,and moment techniques in the operator-product expansion: Equivalence,improved methods,and the heavy quark expansion

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.     

Power-Law Inflation in Spacetimes Without Symmetry

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of de Sitter spacetime and Kaluza-Klein reduction techniques.     

On the implicit integral character of Roothaan's expansion

The molecular generator coordinate Hartree-Fock method is reviewed. The connection between a quadrature solution of the generator coordinate Hartree-Fock equations and Roothaan's equations is stressed. The relation between linear expansion coefficients and generator coordinate weight functions is discussed and a numerical and analytical example is provided for the 1s orbital of the hydrogen atom represented as the integral transform of a Gaussian function. For the same example, the Gauss-Labatto quadrature is employed to emphasize the implicit integral character of Roothaan's equations. As a major conclusion, the interpretation that every LCAO calculation is actually performing integrations of the Griffin-Wheeler equations is advanced. Basis sets are therefore abscissas of the implicit quadrature used in the integration, whereas the linear coefficients automatically incorporate the corresponding weights. Subsequently, it is shown how to extract the generator coordinate weight function from the LCAO coefficients which has the advantage of being a characteristic of the physical system under study and not of the particular calculation being carried out. As such, basis set design becomes how to efficiently sample the weight function. Received: 13 June 1998 / Received in final form: 12 August 1998 / Accepted: 14 September 1998