Simplest cosmological model with the scalar field II. Influence of cosmological constant

Continuing the investigation of the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in closed minisuperspace Friedmann-Robertson-Walker model. The transition from chaotic to regular behaviour for large values of cosmological constant is discussed. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.Comment: 12 pages with 2 gif figures and 2 eps figures, mprocl.sty, To appear in International Journal of Modern Physics

Joint Probabilities Reproducing Three EPR Experiments On Two Qubits

An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.Comment: Typo corrected in abstrac

The Black Di-Ring: An Inverse Scattering Construction

We use the inverse scattering method (ISM) to derive concentric non-supersymmetric black rings. The approach used here is fully five-dimensional, and has the modest advantage that it generalizes readily to the construction of more general axi-symmetric solutions.Comment: v3: 2 subsections added, typos fixed, more refs, journal version. v4: a transcription error in the ADM mass fixe

Cosmological zoo -- accelerating models with dark energy

ecent observations of type Ia supernovae indicate that the Universe is in an accelerating phase of expansion. The fundamental quest in theoretical cosmology is to identify the origin of this phenomenon. In principle there are two possibilities: 1) the presence of matter which violates the strong energy condition (a substantial form of dark energy), 2) modified Friedmann equations (Cardassian models -- a non-substantial form of dark matter). We classify all these models in terms of 2-dimensional dynamical systems of the Newtonian type. We search for generic properties of the models. It is achieved with the help of Peixoto's theorem for dynamical system on the Poincar{\'e} sphere. We find that the notion of structural stability can be useful to distinguish the generic cases of evolutional paths with acceleration. We find that, while the $\Lambda$CDM models and phantom models are typical accelerating models, the cosmological models with bouncing phase are non-generic in the space of all planar dynamical systems. We derive the universal shape of potential function which gives rise to presently accelerating models. Our results show explicitly the advantages of using a potential function (instead of the equation of state) to probe the origin of the present acceleration. We argue that simplicity and genericity are the best guide in understanding our Universe and its acceleration.Comment: RevTeX4, 23 pages, 10 figure

On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity

It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha$, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha=0, \sqrt 3$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha=0, \sqrt 3$. This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.Comment: v2: 23 pages, typos corrected, minor modifications, to appear in CQ

Soliton solution in dilaton-Maxwell gravity

The inverse scattering problem method application to construction of exact solution for Maxwell dilaton gravity system ia considered. By use of Belinsky and Zakharov L - A pair the solution of the theory is constructed. The rotating Kerr - like configuration with NUT - parameter is obtained.Comment: 8 pages in LaTex; published in Gen. Rel. Grav. pp. 32 (2000) 2219-222

On the interaction of a single-photon wave packet with an excited atom

The interaction of a single-photon wave packet with an initially excited two-level atom in free space is studied in semiclassical and quantum approaches. It is shown that the final state of the field does not contain doubly occupied modes. The process of the atom's transition to the ground state may be accelerated, decelerated or even reversed by the incoming photon, depending on parameters. The spectrum of emitted radiation is close to the sum of the spectrum of the incoming single-photon wave packet and the natural line shape, with small and complicated deviations.Comment: 17 pages, 5 figure

Scalar Field Probes of Power-Law Space-Time Singularities

We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde

Distorted 5-dimensional vacuum black hole

In this paper we study how the distortion generated by a static and neutral distribution of external matter affects a 5-dimensional Schwarzschild-Tangherlini black hole. A solution representing a particular class of such distorted black holes admits an RxU(1)xU(1) isometry group. We show that there exists a certain duality transformation between the black hole horizon and a stretched singularity surfaces. The space-time near the distorted black hole singularity has the same topology and Kasner exponents as those of a 5-dimensional Schwarzschild-Tangherlini black hole. We calculate the maximal proper time of free fall of a test particle from the distorted black hole horizon to its singularity and find that, depending on the distortion, it can be less, equal to, or greater than that of a Schwarzschild-Tangherlini black hole of the same horizon area. This implies that due to the distortion, the singularity of a Schwarzschild-Tangherlini black hole can come close to its horizon. A relation between the Kretschmann scalar calculated on the horizon of a 5-dimensional static, asymmetric, distorted black hole and the trace of the square of the Ricci tensor of the horizon surface is derived.Comment: 20 pages, 9 figure

Polarization ququarts

We discuss the concept of polarization states of four-dimensional quantum systems based on frequency non-degenerate biphoton field. Several quantum tomography protocols were developed and implemented for measurement of an arbitrary state of ququart. A simple method that does not rely on interferometric technique is used to generate and measure the sequence of states that can be used for quantum communication purposes.Comment: 13 pages, 10 figure