The Petrov and Kaigorodov-Ozsv\'ath Solutions: Spacetime as a Group Manifold

The Petrov solution (for $\Lambda=0$) and the Kaigorodov-Ozsv\'ath solution (for $\Lambda<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for the Kaigorodov-Ozsv\'ath solution in the context of the adS/CFT correspondence. By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group. The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsv\'ath solution. By applying the method of non-linear realisations to both algebras, we obtain a Lagrangian of Finsler type from the general first-order action in both cases. Interpreting the Petrov solution as the exterior solution of a rigidly rotating dust cylinder, we discuss the question of creation of CTCs by spinning up such a cylinder. We show geodesic completeness of the Petrov and Kaigorodov-Ozsv\'ath solutions and determine the behaviour of geodesics in these spacetimes. The holonomy groups were shown to be given by the Lorentz group in both cases.Comment: 25 pages (latex), 3 figures, corrected a few minor error

Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity

We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.Comment: REVTEX4, 8 pages, no figures, added 2 references and a few clarifying remark

The structure of cool accretion disc in semidetached binaries

We present the results of qualitative consideration of possible changes occurring during the transition from the hot accretion disc to the cool one. We argue the possible existence of one more type of spiral density waves in the inner part of the disc where gasdynamical perturbations are negligible. The mechanism of formation of such a wave as well as its parameters are considered. We also present the results of 3D gasdynamical simulation of cool accretion discs. These results confirm the hypothesis of possible formation of the spiral wave of a new, "precessional" type in the inner regions of the disc. Possible observational manifestations of this wave are discussed.Comment: LaTeX, 16 pages, 8 figures, to be published in Astron. Z

Peculiarities of acid-base properties of peat formed in various agroclimatic zones of the Altai mountainous region

The results of the study of acid-base indicators of peat in the Altai mountainous region are presented. The natural factors that in the aggregate determine the peculiarities of the physicochemical properties of mountain peat of different agro-climatic zones of the Altai Mountains have been revealed. The variation in the acid values, total absorbed bases, adsorption capacity and the degree of saturation of raised-bog, transitional, fen peat, the number of exchangeable ions Са2+ and Mg2+ has been estimated. The interrelation among these indicators has been presented. For the first time, regression equations of the relationship between exchangeable acidity рНKCl and the degree of peat base saturation V, between total absorbed bases S and the degree of peat base saturation V have been obtained using nonlinear regression analysis. The adequacy and stability of the developed models have been verified. The calculated mean errors of approximation of regression models characterise the high accuracy of the forecast and are indicative of a good selection of models for the initial data

A model of superoutbursts in binaries of SU UMa type

A new mechanism explaining superoutbursts in binaries of SU UMa type is proposed. In the framework of this mechanism the accretion rate increase leading to the superoutburst is associated with formation of a spiral wave of a new "precessional" type in inner gasdynamically unperturbed parts of the accretion disc. The possibility of existence of this type of waves was suggested in our previous work (astro-ph/0403053). The features of the "precessional" spiral wave allow explaining both the energy release during the outburst and all its observational manifestations. The distinctive characteristic of a superoutburst in a SU UMa type star is the appearance of the superhump on the light curve. The proposed model reproduces well the formation of the superhump as well as its observational features, such as the period that is 3-7% longer than the orbital one and the detectability of superhumps regardless of the binary inclination.Comment: LaTeX, 20 pages, 4 figures, to be published in Astron. Z

Solvegeometry gravitational waves

In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein solvmanifolds (i.e., solvable Lie groups considered as manifolds) constructed in a previous paper as a starting point, we show that there also exist solvegeometry gravitational waves. Some geometric aspects are discussed and examples of spacetimes having additional symmetries are given, for example, spacetimes generalising the Kaigorodov solution. The solvegeometry gravitational waves are also examples of spacetimes which are indistinguishable by considering the scalar curvature invariants alone.Comment: 10 pages; v2:more discussion and result

\delta-derivations of n-ary algebras

We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraically closed field zero characteristic, and simple ternary Malcev algebra M_8. We constructed new examples of non-trivial \delta-derivations of Filippov algebras and new examples of non-trivial antiderivations of simple Filippov algebras.Comment: 12 page

Embeddings in Non-Vacuum Spacetimes

A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless scalar field are also discussed. The embedding procedures are illustrated with a number of examples.Comment: 17 pages, Plain Latex. Extended discussion on embeddings with scalar fields and further examples included. In press, Classical and Quantum Gravit

Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe

The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the space-times represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the 'background' space is not asymptotically flat and requires a 'rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov space-time, which is the simplest representative of the Siklos class, is analyzed in more detail. It is argued that it may serve as a 'cosmological' analogue of the well-known homogeneous pp-waves in the flat universe.Comment: 17 pages, to be published in Class. Quantum Gravit

Universal time-dependent deformations of Schrodinger geometry

We investigate universal time-dependent exact deformations of Schrodinger geometry. We present 1) scale invariant but non-conformal deformation, 2) non-conformal but scale invariant deformation, and 3) both scale and conformal invariant deformation. All these solutions are universal in the sense that we could embed them in any supergravity constructions of the Schrodinger invariant geometry. We give a field theory interpretation of our time-dependent solutions. In particular, we argue that any time-dependent chemical potential can be treated exactly in our gravity dual approach.Comment: 24 pages, v2: references adde