Vacuum energy and inertial dragging

We investigate if there is any inertial dragging effect associated with vacuum energy. Spacetime inside and outside a rotating thin shell, as well as the mechanical properties of the shell, are analyzed by means of Israel's general relativistic theory of surface layers. Our investigation generalizes that of Brill and Cohen, who found vacuum-solutions of Einstein's field equations (with vanishing cosmological constant), inside and outside a rotating shell. We include a nonvanishing vacuum-energy inside the shell. It is found that the inertial dragging angular velocity increases with increasing density of vacuum energy.     

Kaluza-Klein theory and Dirac equation in higher dimensional Riemann-Cartan space

The higher dimensional Kaluza-Klein theory in Riemann-Cartan space is discussed. To clarify its implications, we investigate the simplest five-dimensional case of the theory in detail. The Einstein-like, Maxwell, and Dirac equations in four-dimensional space-time are obtained by reducing the corresponding five-dimensional field equations. The effect of spin-spin interaction induced by torsion is revealed by analyzing the Dirac equation in this case.     

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.     

Plane-wave solutions in five-dimensional Kaluza-Klein theories

Exact solutions representing mixed plane-electromagnetic and planegravitational waves in five-dimensional Kaluza-Klein theories are obtained. Two extreme cases, corresponding to the plane waves of the four-dimensional Einstein-Maxwell theory and the dilation waves, respectively, are discussed. In addition, it is found that the five-dimensional harmonic condition is reduced to the usual four-dimensional harmonic condition plus the Lorentz condition.     

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.     

The Kaluza-Klein theory and four-dimensional spacetime

The conventional electromagnetism, which includes Maxwell's field equations and the Lorentz force relation, does not provide an explanation of well-known electromagnetic phenomena, such as the Aharonov-Bohm interference effect and the Meissner-Ochsenfeld effect in superconductors. In this paper, it is shown that the Kaluza-Klein five-dimensional theory suggests a simple explanation of these effects on a unified basis.     

Five-dimensional Kaluza-Klein black holes coupled to massive scalar particles

Spherically symmetric solutions coupled to massive scalar particles in five-dimensional Kaluza-Klein theory are obtained. The solutions contain two event horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer one is a new horizon which is produced by the massive scalar particles. It is found that the massive modes contribute an effective cosmological constant to the four-dimensional Einstein theory.     

High-energy approximations to nuclear scattering: W. E. Frahn and B. Schürmann. Physics Department,University of Cape Town,Rondebosch (Cape), South Africa

The effect of slow rotation on the dipole magnetic field of neutron stars is studied. It is shown that the differential rotation of inertial frames produced by the effect of “dragging of inertial frames” induces an additional component of electric field outside the star. This new component, as well as the usual electromagnetic components, vanishes as in the limit of collapse of a star to its Schwarzschild radius. For typical neutron stars, the electric quadrupole moment is about half that obtainable from a flat space analysis.     

Translational inertial dragging

The electrical field inside a uniformly charged, slowly accelerated spherical shell is calculated. The result is used to find the inertial translational dragging field inside a slowly accelerated spherical shell of dust particles, according to the linearized gravitational field equations. The relevance of this effect in connection with Mach's principle and the principle of relativity is discussed.     

Kaluza-Klein space and strong gravity

A study of strong gravity theory is carried out in five-dimensional Kaluza-Klein space-time. A relation between the cosmological constant and the radius parameter of the fifth dimension is obtained. The effect of the extra dimension is seen through the generation of masses simulating a Regge-like mass spectrum. It is found that the confinement mechanism is built into the strong gravity formalism. We also discuss the trapping of quarks in the 5D background.     

Higher-dimensional white holes

White holes (relativistic anticollapsing objects) are considered both in the five-dimensional Kaluza-Klein theory and in the many-dimensional representation of extended space-time manifolds with horizons within the framework of general relativity. In the last model white holes (e.g. Kerr-Newman) appear as anticollapsing from extra (additional) dimensions. These dimensions are connected with the global structure of space-time manifolds.     

Inhomogeneous Kaluza-Klein model with heat flow

We present a cosmological model in Kaluza-Klein spacetime with a matter field obeying an equation of state and a radial heat flow. The (3+1)space resembles that of a Robertson-Walker spacetime, but unlike the corresponding four-dimensional case our five-dimensional spacetime admits a radial flow of heat even when the three-space curvature remains a constant. Further our solution exhibits the desirable feature of dimensional reduction.     

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.     

Experimental determination of the free-fall acceleration of a relativistic charged particle. II. A cylindrical solenoid in a time-independent field of inertial forces

An arbitrarily oriented infinite cylindrical solenoid at rest in a time-independent field of inertial forces is discussed. The problem of the electromagnetic field of such a solenoid is solved. It is shown that there arises inside and outside of the solenoid an electrostatic field associated with the angular velocity of the local reference system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 28–32, 1979.     

Spin matrices for gravitons and the humblet decomposition of the angular momentum of gravitational radiation in the linearized theory

We develop spin matrices for a classical gravitational field in the linearized theory which satisfy angular-momentum commutation relations and are appropriate for a spin angular momentum of two. The same spin matrices come out of a decomposition of the angular momentum density of the linearized gravitational field into orbital and spin parts, similar to that carried out by Humblet for the electromagnetic field. To achieve this decomposition, we use the momentum density for the gravitational field obtained from the Landau-Lifshitz pseudo-tensor in the weak gravity limit. We note a formal connection between the spin angular momenta of gravitational and electromagnetic fields using the Kaluza-Klein idea.     

Quantum effects on higher dimensional space-time

Particle production in an odd-dimensional homogeneous universe with small anisotropy is discussed by using the effective action method. The pair production is a completely non-local phenomenon in an odd-dimensional theory, in contrast to the case of the familiar four-dimensional space-time. The effect of the closedness of the extra-dimensional space, i.e., the Casimir effect, which seems to be important in the scenario of Kaluza-Klein cosmology, is also discussed in the case of five dimensions.     

Large-Scale Two-Dimensional Quantum Fluctuations of Five-Dimensional and Four-Dimensional Space-Time Metrics

Large-scale two-dimensional quantum fluctuations of five-dimensional space-time metric are constructed and the effect of the fluctuations on the nested four-dimensional worlds is studied. In doing so, the fluctuations affect not all four-dimensional worlds but only a part of them. The energy-momentum tensor of four-dimensional space-time has a physical form both in the absence and in the presence of fluctuations; it means that the fluctuations can be realized by real matter. A spatial region occupied by the fluctuations constructed in this work can be infinitely large and the fluctuations can occur during a long period of time. Therefore, we refer to these fluctuations as large-scale fluctuations.     

电磁能量-动量转化和守恒定律四维形式的一种推导

定义了电磁场的四维动量流密度张量,并将电磁能量转化和守恒定律及动量转化和守恒定律写成了四维协变形式,给出了三维电磁能量密度、能流密度、动量密度和动量流密度关于两个惯性系之间的变换关系,还给出了四维动量流密度张量与四维电磁场张量之间的依赖关系。     

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.     

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.