Шляхи подолання банкрутства комерційних банків України

Кайгородов О. М. Шляхи подолання банкрутства комерційних банків України / О. М. Кайгородов // Економіко-правовий розвиток сучасної України : матер. ІIІ Всеукр. наук. конф. студ., аспір. та молодих вчених (22-23 листопада 2013 р., м. Одеса) / за ред. д.е.н., проф. О. М. Кібік, д.ю.н., проф. О. П. Подцерковного ; Національн. ун-т «Одеська юридична академія» – Одеса : Фенікс, 2013. – С. 57-60

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

Holographic flows to IR Lifshitz spacetimes

Recently we studied `vanishing' horizon limits of `boosted' black D3-brane geometry \cite{hsnr}. The type IIB solutions obtained by taking these special double limits were found to describe nonrelativistic Lifshitz spacetimes at zero temperature. In the present work we study these limits for TsT black-hole solutions which include $B$-field. The new Galilean solutions describe a holographic RG flow from Schr\"odinger ($a=2$) spacetime in UV to a Lifshitz universe ($a=3$) in the IR.Comment: 10 pages; v2: A bad typo in eq.8 corrected; v3: Discussion and reference on Kaigorodov spaces included, correction in sec-3, to be published in JHE

Lifshitz/Schr\"odinger D-p-branes and dynamical exponents

We extend our earlier study of special double limits of `boosted' $AdS_5$ black hole solutions to include all black D$p$-branes of type II strings. We find that Lifshitz solutions can be obtained in generality, with varied dynamical exponents, by employing these limits. We then study such double limits for `boosted' D$p$-brane bubble solutions and find that the resulting non-relativistic solutions instead describe Schr\"odinger like spacetimes, having varied dynamical exponents. We get a simple map between these Lifshitz & Schr\"odinger solutions and a relationship between two types of dynamical exponents. We also discuss about the singularities of the Lifshitz solutions and an intriguing thermodynamic duality.Comment: 20 pages; 3 figures; v3: similar to JHE

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

Supergravity Duals to the Noncommutative N=4 SYM theory in the Infinite Momentum Frame

In this work the construction of supergravity duals to the noncommutative ${\cal N}=4$ SYM theory in the infinite momentum frame but with constant momentum density is attempted. In the absence of the content of noncommutativity, it has been known for some time that the previous $AdS_{5}/CFT_{4}$ correspondence should be replaced by the $K_{5}/CFT_{4}$ (with $K_{(p+2)}$ denoting the generalized Kaigorodov spacetime) correspondence with the pp-wave propagating on the BPS brane worldvolume. Interestingly enough, putting together the two contents, i.e., the introduction of noncommutativity and at the same time that of the pp-wave along the brane worldvolume, leads to quite nontrivial consequences such as the emergence of ``time-space'' noncommutativity in addition to the ``space-space'' noncommutativity in the manifold on which the dual gauge theory is defined. Taking the gravity decoupling limit, it has been realized that for small $u$, the solutions all reduce to $K_{5}\times S^5$ geometry confirming our expectation that the IR dynamics of the dual gauge theory should be unaffected by the noncommutativity while as $u\to \infty$, the solutions start to deviate significantly from $K_{5}\times S^5$ limit indicating that the UV dynamics of the dual gauge theory would be heavily distorted by the effect of noncommutativity.Comment: 21 pages, Latex, One expression changed, a reference added, to appear in Phys. Rev.

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

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

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