Lax pair tensors and integrable spacetimes

The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation -- the three-particle open Toda lattice -- is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.Comment: 10 pages, LaTe

Generalized plane-fronted gravitational waves in any dimension

We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for an arbitrary cosmological constant.Comment: Revtex, 18 pages, no figure

Energy-momentum and angular momentum of Goedel universes

We discuss the Einstein energy-momentum complex and the Bergmann-Thomson angular momentum complex in general relativity and calculate them for space-time homogeneous Goedel universes. The calculations are performed for a dust acausal model and for a scalar-field causal model. It is shown that the Einstein pseudotensor is traceless, not symmetric, the gravitational energy is "density" is negative and the gravitational Poynting vector vanishes. Significantly, the total (gravitational and matter) energy "density" fro the acausal model is zero while for the casual model it is negative.The Bergmann-Thomson angular momentum complex does not vanish for both G\"odel models.Comment: an amended version, 24 pages, accepted to PR

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2

Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.Comment: 29 page

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

New solutions in 3D gravity

We study gravitational theory in 1+2 spacetime dimensions which is determined by the Lagrangian constructed as a sum of the Einstein-Hilbert term plus the two (translational and rotational) gravitational Chern-Simons terms. When the corresponding coupling constants vanish, we are left with the purely Einstein theory of gravity. We obtain new exact solutions for the gravitational field equations with the nontrivial material sources. Special attention is paid to plane-fronted gravitational waves (in case of the Maxwell field source) and to the circularly symmetric as well as the anisotropic cosmological solutions which arise for the ideal fluid matter source.Comment: Revtex, 21 pages, no figure

M-theory on a Time-dependent Plane-wave

We propose a matrix model on a homogeneous plane-wave background with 20 supersymmetries. This background is anti-Mach type and is equivalent to the time-dependent background. We study supersymmetries in this theory and calculate the superalgebra. The vacuum energy of the abelian part is also calculated. In addition we find classical solutions such as graviton solution, fuzzy sphere and hyperboloid.Comment: 19pages, no figures, LaTeX, JHEP3.cl

Teeth of the red fox Vulpes vulpes (L., 1758) as a bioindicator in studies on fluoride pollution

An examination was made of fluoride content in the mandibular first molars of the permanent teeth of the red fox Vulpes vulpes living in north-west (NW) Poland. The teeth were first dried to a constant weight at 105°C and then ashed. Fluorides were determined potentiometrically, and their concentrations were expressed in dry weight (DW) and ash. The results were used to perform an indirect estimation of fluoride pollution in the examined region of Poland. The collected specimens (n = 35) were classified into one of the three age categories: immature (im, 6–12 months), subadult (subad, from 12 to 20 months) and adult (ad, >20 months). The mean concentrations (geometric mean) of fluoride were similar in the im and subad groups (230 and 296 mg/kg DW and 297 and 385 mg/kg ash, respectively), and significantly smaller than in the ad group (504 and 654 mg/kg, respectively, in DW and ash). Basing on other reports that the ∼400 mg/kg DW concentration of fluoride in bones in the long-lived wild mammals generally reflects the geochemical background, it was found that 57% of the foxes in NW Poland exceeded this value by 9% to 170%. This indirectly reflects a moderate fluoride contamination in the tested region