Axisymmetric electrovacuum spacetimes with an additional Killing vector and radiation

Main results concerning allowable additional symmetries of axially symmetric electrovacuum spacetimes are summarized. These are translational Killing vectors and the boost Killing vector. However, this is only the boost symmetry that does not exclude radiation and permit a spacetime to be asymptotically flat with global null infinity.Comment: 2 pages, contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200

Curvature invariants in algebraically special spacetimes

It is well known that all curvature invariants of the order zero vanish for type-III and type-N vacuum spacetimes. We briefly summarize properties of higher order curvature invariants for these spacetimes.Comment: 2 pages, contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200

Radiative fields in spacetimes with Minkowski and de Sitter asymptotics

The classical Bondi-Penrose approach to the gravitational radiation theory in asymptotically flat spacetimes is recalled and recent advances in the proofs of the existence of such spacetimes are briefly reviewed. We then mention the unique role of the boost-rotation symmetric spacetimes, representing uniformly accelerated objects, as the only explicit radiative solutions known which are asymptotically flat; they are used as test beds in numerical relativity and approximation methods. The main part of the review is devoted to the examples of radiative fields in the vacuum spacetimes with positive cosmological constant. Type N solutions are analyzed by using the equation of geodesic deviation. Both these and Robinson-Trautman solutions of type II are shown to approach de Sitter universe asymptotically. Recent work on the the radiative fields due to uniformly accelerated charges in de Sitter spacetime ("cosmological Born's solutions") is reviewed and the properties of these fields are discussed with a perspective to characterize general features of radiative fields near a de Sitter-like infinity.Comment: 23 pages, invited talk, 10th Greek Relativity Meeting, Chalkidiki, May 200

Design of Dual Bandpass and Bandreject LC Ladder Filters

This paper deals with the design of two-passband bandpass and two-stopband bandreject LC ladder filters. The design method is based on the special dual frequency transformation that transforms normalized lowpass to either bandpass with two passbands or to bandreject with two stopbands that are specified by four cutoff frequencies. The paper shows analytical solution relating these four cutoff frequencies to parameters of dual frequency transformation. It enables a direct computation of dual band LC filter elements from a normalized lowpass filter by means of simple relations. These relations have been implemented in the mathematical program Maple (TM) as new user functions. They are supposed to be used as an enhancement of Syntfil package which is intended for analog filter design in program Maple. Specific application is shown on an example of the two-passband bandpass LC filter design

Creativity in Science: Historical Illustrations and the Academic Paradigm

Koestler identifies creativity in terms of the ability of the individual to make analogies, the ability to recognize relationships between apparently unrelated events. Joseph Lister struggled with the unknown cause of sepsis, gangrene and suppuration in surgical wounds. Ignaz Philipp Semmelweis was immersed in his work to determine the cause of puerperal fever. Of many creative giants in the history of science, Walker places Pasteur among the best for his astonishing ability for seeing the salient factors of a problem. Boyer relates scholarship and creativity to academics who carry on research, publish, and perhaps relay to their students what they have discovered. Creativity is not easily defined nor explained, but the history of scientific discovery has provided some clues as to the nature of the creative person

Isofrequency pairing of geodesic orbits in Kerr geometry

Abstract ? Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum, and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal, and (mean) azimuthal motions. Here, we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair, the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain “synchronized” in phase.<br/

Note on Invariants of the Weyl Tensor

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.Comment: 3 pages, no figures, corrected expression (12

Magnetized Black Hole on Taub-Nut Instanton

We present an exact solution to the 5D Einstein-Maxwell-dilaton equations describing a static black hole on Taub-Nut instanton. By construction the solution does not possess a charge, but is magnetized along the compact dimension. As a limit we obtain a new regular solution representing a magnetized Kaluza- Klein monopole. We investigate the relevant physical properties and derive the Smarr-like relations.Comment: 14 pages, 1 figur