Algebraically special vacuum gravitational fields with a cosmological constant

A general view is given of the Petrov type II metric with a cosmological constant to an accuracy of two complex functions of three variables which are related by four differential equations. As a consequence the form of the metric is obtained for types III and N which are specified by one complex function satisfying three differential equations. A particular solution is given as an example of an accurate solution of type II with a cosmological constant. State University, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 102–108, June, 1996.     

Algebraically special,nonaligned, non-null Einstein-Maxwell fields

A class of algebraically special non-null electrovac solutions is presented, in which the repeated principal null congruence is shear free, twist free, and geodesic, and is not aligned with a principal null direction of the electromagnetic field. This class includes all previously known solutions of this type as special cases. It can also be considered as a generalization of the Robinson-Trautman family of solutions.     

Algebraically special gravitational fields with single-parameter motion groups

The Newman—Penrose equations for the general class of algebraically special gravitational fields with both nonzero and zero cosmological constants are reduced for gravitational fields outside of the field sources. Then new classes of exact solutions of the nondegenerate Petrov II type are derived under the additional requirement that a single-parameter group of isometric motions exist. Kazan' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 75–81, May, 1996.     

Algebraically special left-flat spaces and their associated space-times

In a recent paper it was shown how to construct, under certain circumstances, asymptotic (Newman-Unti) series expansions for the spin-coefficient variables for real space-times from data obtained from a given left-flat space in an appropriate frame. If these expansions represent asymptotically flat space-times the latter have the given left-flat space as their H space. The method was described in a frame in which the asymptotic left-shear was zero whereas was not. For the discussion of algebraically special left-flat spaces it is more convenient to have vanish and remain nonzero. In this paper we determine all algebraically special left-flat spaces with diverging rays, utilizing Penrose's conformal technique, and then show in detail how to find the “initial data” for the construction of asymptotic series expansions for the corresponding real space-times.     

Acceleration of charged particles and radiation reaction III: Motion in pulsar vacuum fields

We derive an analytic solution for particle motion in strong, linearily polarized spherical waves for the case of negligible radiation reaction. If radiation reaction is included the initial part of the motion can also be described analytically, whereas the further motion is obtained from a numerical integration of the equation of motion.     

Instantons and transverse pure gauge fields

The phenomenon of the ambiguity of the Coulomb gauge in Yang-Mills theories, first discovered by Gribov, is studied for the instanton solutions.It is shown that in the Coulomb gauge the instanton connects a non-vanishing transverse pure gauge field in the remote (Euclidean) past to an analogous one in the far future.     

Inertial mass and the quantum vacuum fields

Even when the Higgs particle is finally detected, it will continue to be a legitimate question to ask whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter. General relativity specifies which geodesic path a free particle will follow, but geometrodynamics has no mechanism for generating a reaction force for deviation from geodesic motion. We discuss a different approach involving the electromagnetic zero‐point field (ZPF) of the quantum vacuum. It has been found that certain asymmetries arise in the ZPF as perceived from an accelerating reference frame. In such a frame the Poynting vector and momentum flux of the ZPF become non‐zero. Scattering of this quantum radiation by the quarks and electrons in matter can result in an acceleration‐dependent reaction force. Both the ordinary and the relativistic forms of Newton's second law, the equation of motion, can be derived from the electrodynamics of such ZPF‐particle interactions. Conjectural arguments are given why this interaction should take place in a resonance at the Compton frequency, and how this could simultaneously provide a physical basis for the de Broglie wavelength of a moving particle. This affords a suggestive perspective on a deep connection between electrodynamics, the origin of inertia and the quantum wave nature of matter.     

Coupled chains in electric and magnetic fields revisited

Coupled chains in electric and magnetic fields are discussed in terms of interplays between periodicity conditions and the factorization of the wavefunction in the wavenumber representation. Proceeding in this manner yields a quickly tractable matching condition providing the quantization rule to the alternative derivation of complex energy bands. Besides achieving a deeper understanding of Wannier-Stark ladders in terms of complex resonance energies, we now have the opportunity to establish related energy levels by resorting to a suitable conversion technique. This amounts to perform an immediate integration of such energy bands over the Brillouin-zone. Such energy levels exhibit, this time, a safe dependence on the chain parameter. Dynamic localization effects, conserved currents and stripe conductivity formulae have also been discussed.     

Local duality, chiral supersymmetry and fermion-like formulation of non-Abelian pure gauge fields

This work generalizes the fermion-like formulation of the Maxwell theory to the non-Abelian Yang–Mills theory without matter fields. This is a new representation of the Lie algebra valued electric and magnetic fields. The resulting equations of motion are invariant under the chiral transformation. In this formulation, duality is a kind of chirality. We may also define local duality transformations in terms of space-time dependent parameters. There is an N=1 supersymmetry for the Dirac-like operator in this representation. Received: 19 June 2000 / Revised version: 10 October 2000 / Published online: 15 March 2001     

Review of radiation sources,calibration facilities and simulated workplace fields

A review on radiation sources, calibration facilities and realistic fields is presented and examples are given. The main characteristics of the fields are shortly described together with their domain of applications. New emerging fields are also mentioned and the question of needs for additional calibration fields is raised.     

A Note on Algebraically Special,Asymptotically Simple and Empty Spacetime

It is proved that subject to certain physically reasonable restrictions on the curvature of spacetime, an algebraically special, asymptotically simple and empty spacetime is necessarily a copy of the Minkowski space. This imposes further requirements a nontrivial asymptotically simple and empty spacetime has to satisfy.     

Frame-dragging fields and spin 1 gravitomagnetic radiation

Experimental results published in 2004 (Ciufolini and Pavlis in Nature 431:958–960, 2004) and 2011 (Everitt et al. in Phys Rev Lett 106:221101, 1–5, 2011) have confirmed the frame-dragging phenomenon for a spinning earth predicted by Einstein’s field equations. Since this is observed as a precession caused by the gravitomagnetic (GM) field of the rotating body, these experiments may be viewed as measurements of a GM field. The effect is encapsulated in the classic steady state solution for the vector potential field $\zeta $ of a spinning sphere–a solution applying to a sphere with angular momentum J and describing a field filling space for all time (Weinberg in Gravitation and Cosmology, Wiley, New York, 1972). In a laboratory setting one may visualise the case of a sphere at rest $(\zeta =0, \text{ t}<0)$ , being spun up by an external torque at $\text{ t}=0$ to the angular momentum J: the $\zeta $ field of the textbook solution cannot establish itself instantaneously over all space at $\text{ t}=0$ , but must propagate with the velocity c, implying the existence of a travelling GM wave field yielding the textbook $\zeta $ field for large enough t (Tolstoy in Int J Theor Phys 40(5):1021–1031, 2001). The linearized GM field equations of the post-Newtonian approximation being isomorphic with Maxwell’s equations (Braginsky et al. in Phys Rev D 15(6):2047–2060, 1977), such GM waves are dipole waves of spin 1. It is well known that in purely gravitating systems conservation of angular momentum forbids the existence of dipole radiation (Misner et al. in Gravitation, Freeman & Co., New York, 1997); but this rule does not prohibit the insertion of angular momentum into the system from an external source–e.g., by applying a torque to our laboratory sphere.     

On conformally flat and type N pure radiation metrics

We study pure radiation spacetimes of algebraic types O and N with a possible cosmological constant. In particular, we present explicit transformations which put these metrics, that were recently re-derived by Edgar, Vickers and Machado Ramos, into a general Ozsváth–Robinson–Rózga form. By putting all such metrics into the unified coordinate system we confirm that their derivation based on the GIF formalism is correct. We identify only few trivial differences.