The Mathematics of Growth Against Limits

The single step growth against limit equation is introduced and its consequences (s curves) are briefly explored. The possibility of sudden jumps (violations) from one growth limit curve to another is recognized and formulated. The full model featuring stochastic violations is developed. An integral equation governing the time evolution of probability density of growth is derived. The integral equation is reduced to a dispersion relation which is used to calculate the velocities of the first three moments of the growth probability density. The improvements in airliner performance over the years is analyzed by decomposition of certain economic data against the models parameters

Polarimetry of an Intermediate-age Open Cluster: NGC 5617

We present polarimetric observations in the UBVRI bands of 72 stars located in the direction of the medium age open cluster NGC 5617. Our intention is to use polarimetry as a tool membership identification, by building on previous investigations intended mainly to determine the cluster's general characteristics rather than provide membership suitable for studies such as stellar content and metallicity, as well as study the characteristics of the dust lying between the Sun and the cluster. The obsevations were carried out using the five-channel photopolarimeter of the Torino Astronomical Observatory attached to the 2.15m telescope at the Complejo Astron\'omico El Leoncito (CASLEO; Argentina. We are able to add 32 stars to the list of members of NGC 5617, and review the situation for others listed in the literature. In particular, we find that five blue straggler stars in the region of the cluster are located behind the same dust as the member stars are and we confirm the membership of two red giants. The proposed polarimetric memberships are compared with those derived by photometric and kinematical methods, with excellent results. Among the observed stars, we identify 10 with intrinsic polarization in their light. NGC 5617 can be polarimetrically characterized with $P_{max}= 4.40$ and $\theta_{v}= 73^\circ.1$. The spread in polarization values for the stars observed in the direction of the cluster seems to be caused by the uneven distribution of dust in front of the cluster's face. Finally, we find that in the direction of the cluster, the interstellar medium is apparently free of dust, from the Sun's position up to the Carina-Sagittarius arm, where NGC 5617 seems to be located at its farthest border

Penrose Limits, the Colliding Plane Wave Problem and the Classical String Backgrounds

We show how the Szekeres form of the line element is naturally adapted to study Penrose limits in classical string backgrounds. Relating the "old" colliding wave problem to the Penrose limiting procedure as employed in string theory we discuss how two orthogonal Penrose limits uniquely determine the underlying target space when certain symmetry is imposed. We construct a conformally deformed background with two distinct, yet exactly solvable in terms of the string theory on R-R backgrounds, Penrose limits. Exploiting further the similarities between the two problems we find that the Penrose limit of the gauged WZW Nappi-Witten universe is itself a gauged WZW plane wave solution of Sfetsos and Tseytlin. Finally, we discuss some issues related to singularity, show the existence of a large class of non-Hausdorff solutions with Killing Cauchy Horizons and indicate a possible resolution of the problem of the definition of quantum vacuum in string theory on these time-dependent backgrounds.Comment: Some misprints corrected. Matches the version in print. To appear in Classical & Quantum Gravit

On the Entropy and the Density Matrix of Cosmological Perturbations

We look at the transition to the semiclassical behaviour and the decoherence process for the inhomogeneous perturbations in the inflationary universe. Two different decoherence mechanisms appear: one dynamical, accompanied with a negligible, if at all, entropy gain, and the other, effectively irreversible dephasing, due to a rapid variation in time of the off-diagonal density matrix elements in the post-inflationary epoch. We thus settle the discrepancies in the entropy content of perturbations evaluated by different authors.Comment: LaTeX2e with the epsf packag

Gravitational Optics: Self-phase modulation and harmonic cascades

Nonlinear wave interaction of low amplitude gravitational waves in flat space-time is considered. Analogy with optics is established. It is shown that the flat metric space-time is equivalent to a centro-symmetric optical medium, with no second order susceptibility. The lowest order nonlinear effects are those due to the third order nonlinearity and include self-phase modulation and high harmonic generation. These processes lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range.Comment: 12 pages, REVTEX

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

On the evolution of a large class of inhomogeneous scalar field cosmologies

The asymptotic behaviour of a family of inhomogeneous scalar field cosmologies with exponential potential is studied. By introducing new variables we can perform an almost complete analysis of the evolution of these cosmologies. Unlike the homogeneous case (Bianchi type solutions), when k^2<2 the models do not isotropize due to the presence of the inhomogeneitiesComment: 23 pages, 1 figure. Submitted to Classical and Quantum Gravit

The stability of Killing-Cauchy horizons in colliding plane wave space-times

It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes occur in space-times representing the collision and subsequent interaction of plane gravitational waves in a Minkowski background, are unstable with respect to bounded perturbations of the initial waves, at least for the case in which the initial waves have constant aligned polarizations.Comment: 8 pages. To appear in Gen. Rel. Gra

Inhomogeneous Einstein-Rosen String Cosmology

Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VI_h cosmology. The asymptotic behaviour of the solutions is investigated and further applications are briefly discussed.Comment: Minor extension of concluding section; 18 pages, to appear in Phys.Rev.