Uniqueness of rotating charged black holes in five-dimensional minimal gauged supergravity

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing–Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong–Cvetič–Lü–Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.     

Black Hole Formation by Canonical Dynamics of Gravitating Shells: An Equatorial View

Gravitating shells lead to simple minisuperspacemodels of black hole formation by gravitational collapseof matter. I interpret here the Hajicek–Kijowskivariational principle for spacetime with a shell as a Dirac–ADM action principle along atimelike foliation including the shell as a leaf. Byreducing this action by spherical symmetry, I obtain theHamiltonian constraint of a collapsing dust shell and use it as a prelude to canonicalquantization.     

Topological Solutions in the Self-dual Chern–Simons–Higgs Theory in a Background Metric

In this Letter we show the existence of topological multi-vortex solutions in the self-dual Chern–Simons–Higgs theory in a background metric which interpolates flat spacetime and cylinder smoothly.     

Dust ion-acoustic wave oscillations in single-walled carbon nanotubes

In this paper, a charged single-walled carbon nanotube that surrounded by charged nanoparticles is modeled as a cylindrical shell of electron–ion–dust plasma. By employing the fluid theory for electron–ion–dust plasma, the dispersion relation of the dust ion-acoustic wave oscillations in the composed system is studied. For negatively charged dust particles, with increasing dust charge density, the phase velocity of the dust ion-acoustic wave will increase in comparison to the pure ion-acoustic wave oscillations.     

Inverse problem of relativistic mechanics for a test charge in an external static field

We consider the motion of an electrically charged test particle in static spacetime when it is necessary to reconstruct the electromagnetic field tensor. The problem is solved for the two special cases when the electromagnetic field reduces to an electrostatic field or a magnetostatic one. It is shown that the electrostatic field can be determined within a single arbitrary function, and the magnetostatic field within two such functions.Translated from Izvestiya Vysskikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–70, February, 1982.     

Electrodynamics of hyperbolically accelerated charges V. The field of a charge in the Rindler space and the Milne space

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.     

Solenoid Configurations and Gravitational Free Energy of the AdS–Melvin Spacetime

In this paper we explore a solenoid configuration involving a magnetic universe solution embedded in an empty Anti-de Sitter (AdS) spacetime. This requires a non-trivial surface current at the interface between the two spacetimes, which can be provided by a charged scalar field. When the interface is taken to the AdS boundary, we recover the full AdS–Melvin spacetime. The stability of the AdS–Melvin solution is also studied by computing the gravitational free energy from the Euclidean action.     

Non-commutative geometry inspired higher-dimensional charged black holes

We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner–Nordström geometry at large distance, and de Sitter spacetime at short distance. Thermodynamical properties of the black hole are investigated and the form of the Area Law is determined. We study pair creation and show that the upper bound on the discharge time increases with the number of extra dimensions.     

The Conformal Metric Associated with the U(1) Gauge of the Stueckelberg–Schrödinger Equation

We review the relativistic classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelbert–Schrödinger equation. To achieve this, one must introduce a fifth, Lorentz scalar, compensation field, in addition to the four vector fields with compensate the action of the space-time derivatives. A generalized Lorentz force can be derived from the classical Hamilton equations associated with this evolution function. We show that the fifth (scalar) field can be eliminated through the introduction of a conformal metric on the spacetime manifold. The geodesic equation associated with this metric coincides with the Lorentz force, and is therefore dynamically equivalent. Since the generalized Maxwell equations for the five dimensional fields provide an equation relating the fifth field with the spacetime density of events, one can derive the spacetime event density associated with the Friedmann–Robertson–Walker solution of the Einstein equations. The resulting density, in the conformal coordinate space, is isotropic and homogeneous, decreasing as the square of the Robertson–Walker scale factor. Using the Einstein equations, one see that both for the static and matter dominated models, the conformal time slice in which the events which generate the world lines are contained becomes progressively thinner as the inverse square of the scale factor, establishing a simple correspondence between the configurations predicted by the underlying Friedmann–Robertson–Walker dynamical model and the configurations in the conformal coordinates.     

Proca Effect in Reissner–Nordstrom de Sitter Metric

Reissner–Nordstrom de Sitter spacetime with photon rest mass is studied. An iteration method is used to get the metric of this spacetime. In the case of μ → 0, the solution will return to the common Reissner–Nordstrom de Sitter spacetime.     

Quantum Structures in Einstein General Relativity

We introduce the notion of a quantum structure on an Einstein general relativistic classical spacetime M. It consists of a line bundle over M equipped with a connection fulfilling certain conditions. We give a necessary and sufficient condition for the existence of quantum structures and classify them. The existence and classification results are analogous to those of geometric quantisation (Kostant and Souriau), but they involve the topology of spacetime, rather than the topology of the configuration space. We provide physically relevant examples, such as the Dirac monopole, the Aharonov–Bohm effect and the Kerr–Newman spacetime. Our formulation is carried out by analogy with the geometric approach to quantum mechanics on a spacetime with absolute time, given by Jadczyk and Modugno.     

Dynamics of Rotating Cylindrical Shells in General Relativity

Cylindrical spacetimes with rotation are studied using the Newmann–Penrose formulas. By studying null geodesic deviations, the physical meaning of each component of the Riemann tensor is given. These spacetimes are further extended to include rotating dynamic shells, and the general expression of the surface energy-momentum tensor of the shells is given in terms of the discontinuity of the first derivatives of the metric coefficients. As an application of the developed formulas, a stationary shell that generates the Lewis solutions, which represent the most general vacuum cylindrical solutions of the Einstein field equations with rotation, is studied by assuming that the spacetime inside the shell is flat. It is shown that the shell can satisfy all the energy conditions by properly choosing the parameters appearing in the model, provided that 0 1, where is related to the mass per unit length of the shell. PACS numbers: 04.20Cv, 04.30.+x, 97.60.Sm, 97.60.Lf.     

A critical analysis of Helmholtz's argument against Weber's electrodynamics

We present Helmholtz's argument against Weber's electrodynamics. It is related with a fixed charged nonconducting spherical shell and a charged particle moving inside it. Then we utilize Weber's electrodynamics plus Schrödinger's expression for gravitational interactions in order to obtain the equation of motion and to study this situation. We show that this approach avoids the problems pointed out by Helmholtz. Moreover, it indicates that the effective inertial mass of the charged particle will depend not only on the electrostatic potential of the shell but also on its velocity. This is a relevant aspect of Weber's theory.     

Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background

In this paper, we consider the Casimir energy of massless scalar fields which satisfy the Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.     

Geometrization of the Gauge Connection within a Kaluza–Klein Theory

We geometrize a generic (abelian and non-abelian) gauge coupling within the framework of a Kaluza–Klein theory, by choosing a suitable matter-field dependence on the extra coordinates. We first extend the Nöther theorem to a multidimensional spacetime, the Cartesian product of a 4-dimensional Minkowski space and a compact homogeneous manifold (whose isometries reflect the gauge symmetry). On such a “vacuum” configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra for a spacetime with the Kaluza–Klein restrictions. By splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms arise.     

Spinning Particles in Curved Spacetime

We briefly discuss the relevant equations for the motion of spinning particles in curved spacetime. We describe the generalized Killing equations for spinning spaces and derive the constants of motion. We apply the formalism to solve for the motion of a pseudoclassical spinning particle in Schwarzschild–de Sitter spacetime.     

A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

A refined expression for the Faddeev–Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern–Simons perturbation theory on compact spacetime 3-manifolds with quantisation around an arbitrary flat gauge field isolated up to gauge transformations, pointing out that previous results on the finiteness and formal metric-independence of perturbative expansions of the partition function continue to hold.     

Does Charge Contribute to the Frame Dragging of?Spacetime?

Electrically charged systems bound by a strong gravitational force can sustain a huge amount of electric charge (up to 10²⁰ C) against Coulomb repulsion. General relativistically such systems form a stable hydrostatic configuration both in the non-rotating and rotating cases. Here we study the effects of electric charge (electric energy density) on the spacetime outside a rotating electrically charged system bound by a strong gravitational force. In particular we investigate the effect of charge density on frame-dragging of spacetime in the exterior region. Using the coupled Einstein-Maxwell equations it is found that in the slow rotation approximation charge accumulation not only acts like an additional mass, thus modifying the spherically symmetric part of the spacetime, the electric charge also contributes directly to the dragging of spacetime. A modified Lense-Thirring formula for the spacetime frame dragging frequency is obtained and its implication for rotating charged compact stars is discussed.     

Exact Casimir–Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

We derive the exact Casimir–Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir–Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1R, where R is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.     

Electromagnetic-wave excitation and diffraction by metal cylinder inside flat waveguide

Electromagnetic-wave excitation by a vertical electric dipole located inside a flat waveguide containing a vertical circular metal cylinder is examined. An exact solution is obtained, and the diffracted field inside the waveguide is analyzed. Algorithms are provided for electromagnetic-field calculation in a Rayleigh approximation and in a short-wave approximation. Results of numerical calculations of fields and directivity characteristics are presented. The effect of the cylinder on the radiation power of the dipole in the waveguide is analyzed.Nizhny Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 11, pp. 965–976, November, 1993.