Description of Electromagnetic Radiation Propagating in a Four-Dimensional Space-Time with a Fluctuating Metric Tensor

The effect of spectral broadening of electromagnetic radiation propagating in a four-dimensional space-time with fluctuations in the space curvature caused by relict gravitational radiation is predicted. It is demonstrated that distortion of spectral line profiles of electromagnetic radiation caused by the fluctuating metric is at the level of resolution of the available spectral instrumentation.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Mass hierarchy from many domain walls

We construct a new model with exponential mass hierarchy by starting with the Einstein–Hilbert action with the cosmological constant in five dimensions plus an action describing many domain walls in four dimensions. The model includes many hidden sectors and one visible sector, and each four-dimensional domain wall, that is, 3-brane, interacts with one another through only a gravitational interaction and realizes many universe cosmology inspired by D-brane perspective. It is shown that in the present model only even numbers of domain walls are allowed to locate in five dimensional space-time and the validity of Randall–Sundrum scenario, which explains mass hierarchy between the Planck mass and the electro-weak scale in our world, depends on a relative relation between our world and hidden worlds.     

Study of Branes with Variable Tension

In this work we study a brane world model with variable tension, which gives rise to four-dimensional cosmologies. The brane worlds obtained correspond to E?tv?s branes whose(internal) geometry can be casted as either a four-dimensional(A)dS_4 or a standard radiation period cosmology. The matter dominated period is discussed as well.     

Bäcklund transformations and new solutions of nonlinear wave equations in four-dimensional space-time

Bäcklund transformations for several nonlinear field equations in four-dimensional space-time relating two solutions of the same equation (symmetry), or two different equations (dynamical), are given. These transformations can be used to generate new families of solutions and infinitely many conservation laws for nonlinear equations.Bäcklund transformations and solutions of nonlinear equations have been studied extensively in one-space and one-time dimension. We give here a fairly general method for a class of equations in four-dimensional space-time which paves the way for many further generalizations.Supported in part by the U.S. National Academy of Sciences Foundation Grant No. INT 73-20002 A01 (formerly GF-41958).     

Extensions of the Taub and NUT spaces and extensions of their tangent bundles

A system of extensions of the Taub space and the NUT space with the topology due to Misner is constructed having the property: for each incomplete geodesic in these space-times, there is one and only one extension from the system into which the geodesic smoothly continues. Next, the notion of hypermanifold is introduced which is a generalization of tangent bundle of a space-time, and an untrivial hypermanifold is constructed that contains the tangent bundles of the Taub and NUT spaces as proper submanifolds, and within which almost all geodesics are complete. Locally, the hypermanifolds do not yield anything new, but they provide much broader choice of global properties than any four-dimensional space-time manifold.     

Letter: Constraint Propagation in (N + 1)-Dimensional Space-Time

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for future numerical research of higher-dimensional space-time, we study the dimensional dependence of constraint propagation behavior. The N+1 Arnowitt-Deser-Misner evolution equation has matter terms which depend on N, but the constraints and constraint propagation equations remain the same. This indicates that there would be problems with accuracy and stability when we directly apply the N+1 ADM formulation to numerical simulations as we have experienced in four-dimensional cases. However, we also conclude that previous efforts in re-formulating the Einstein equations can be applied if they are based on constraint propagation analysis.     

An orifice-string in the standard Kaluza-Klein theory

In the standard Kaluza-Klein theory an orifice solution is proposed which can be spliced into a four-dimensional Reissner-Nordstrom space-time. From the point of view of a four-dimensional observer, the obtained orifice solution can be treated as a string moving in a Wheeler superspace of four geometries.Kyrgyz State University, Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 78–81, June, 1993.     

Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.     

Fields with continuously distributed mass

We describe local field theories with continuously distributed mass. Such models can be realized as models in d > 4 space-time with Poincare invariance only in four-dimensional space-time. We also discuss some possible phenomenological consequences. Namely, we show that the Higgs boson phenomenology in the SM extension with continuously distributed Higgs boson mass can differ in a drastic way from the standard Higgs boson phenomenology.     

HYPERKÄHLER STRUCTURE OF THE TAUB-NUT METRIC

The Taub-NUT four-dimensional space-time can be obtained from Euclidean eight-dimensional one through a momentum map construction; the HKLR theorem [9] guarantees the hyperkähler structure of R ⁸ descends to a hyperkähler structure in the Taub-NUT space. Here we present a detailed and fully explicit construction of the hyperkähler structure of a space-time with a Taub-NUT metric.     

Space-time symmetries in the theory of supergravity,IV: Comparison between space-time and superspace formalisms

The two possible definitions, proposed in Parts II and III, of a space-time symmetry in supergravity, arising respectively from an analysis in four-dimensional space-time and from superspace considerations, are shown to be inequivalent, although closely related to one another. It is argued that the former must be preferred to the latter for physical reasons.     

Quantum fluctuations near the classical space-time singularity

The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuationsquantitatively. The cases discussed are (i) the gravitational collapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation nonsingular solutions can occur with finite probabilities.     

Algebraic classification of a bivector in the Kaluza flat space and the magnetic charge

An algebraic classification of a bivector (understood as a generalized electromagnetic field tensor) in the Kaluza flat space-time is presented. It is assumed that a cylindricity condition holds with respect to the fifth coordinate. The concept of a dual rotation that depends on a selected four-dimensional section is introduced in five-dimensional space. By means of this rotation, we are able to relate the stationary gradient magnetic field with the fifth component of the five-dimensional vector potential which, in turn, is associated with a magnetic charge that cannot be observed in four-dimensional space-time. Krasnoyarsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 114–119, January, 1997.     

Production of Dirac particles due to Riccion coupling

It has been noted that at high energy the Ricci scalar is manifested in two different ways, as a matter field as well as a geometrical field (which is its usual nature even at low energy). Here, using the material aspect of the Ricci scalar, its interaction with Dirac spinors is considered in four-dimensional curved space-time. We find that a large number of fermion-antifermion pairs can be produced by the exponential expansion of the early universe.     

Quantum fluctuations in the conformally flat and the schwarzschild space-times

A general technique is described for dealing with the quantum fluctuations between conformally flat space-times. The second part of the paper deals with the Schwarzschild spacetime. It is shown there that this space-time is stable against fluctuations of mass, but transitions between two space-times of different masses can be obtained via conformai fluctuations. Purely conformal fluctuations of the Schwarzschild metric are, however, damped at the event horizon. Similar conclusions are drawn about the Reissner-Nordstrom space-time.     

The structure of groups of motions admitted by Einstein-Maxwell space-times

The known symmetry of the non-null electromagnetic field, which acts as the source of a four-dimensional space-time satisfying the Einstein-Maxwell equations, is used to show that when such a space-time admits a group of motions, generated by a Killing vector, the structure constants for the group must satisfy an additional relation to the known relations of group theory.     

Topological transitions and large-scale structure of space-time in multi-dimensional theory of gravity

The possibility of building a theory of topological transitions within the framework of multidimensional gravitation theories is discussed. It is shown that consideration of a four-dimensional space-time as a submanifold in the space of a large number of measurements provides a real possibility of constructing a theory of the large-scale structure of a four-dimensional physical space-time and, in particular, a theory of topological transitions. The fundamental principles underlying the construction of the theory are expounded. VNIIMS (Scientific-Research Institute of the Metrological Service). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 9–14, February, 1997.     

Bäcklund transformations in four-dimensional space-time

A class of Bäcklund transformations recently introduced for four-dimensional space-time equations is shown to be limited to relating solutions of the sine-Gordon equation.