Weak Sequential Completeness of Uniform Algebras

We prove that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional

Formation of a Black String in a Higher Dimensional Vacuum Gravitational Collapse

We present a solution to the vacuum Einstein Equations which represents a collapse of a gravitational wave in 5 dimensions. Depending on the focal length of the wave, the collapse results, either in a black string covered by a horizon, or in a naked singularity which can be removed.Comment: Minor changes. A reference added. Matches the print version. To appear in Phys. Lett.

Hume, realism, and the infinite divisibility of space

In A Treatise of Human Nature, David Hume offers arguments against the infinite\ud divisibility of space. Some commentators have offered interpretations of these arguments suggesting that a label of ???realist??? or ???materialist??? might apply to Hume???s philosophy. However, a careful reading of the text shows that Hume actually had the opposite intent. These arguments against the infinite divisibility of space demonstrate Hume???s method of examining our ideas and their source impressions to solve philosophical problems. This method serves Hume???s overarching skeptical goals by strictly circumscribing the scope and reach of human knowledge

Power-law expansion in k-essence cosmology

We study spatially flat isotropic universes driven by k-essence. It is shown that Friedmann and k-field equations may be analytically integrated for arbitrary k-field potentials during evolution with a constant baryotropic index. It follows that there is an infinite number of dynamically different k-theories with equivalent kinematics of the gravitational field. We show that there is a large "window" of stable solutions, and that the dust-like behaviour separates stable from unstable expansion. Restricting to the family of power law solutions, it is argued that the linear scalar field model, with constant function F, is isomorphic to a model with divergent speed of sound and this makes them less suitable for cosmological modeling than the non-linear k-field solutions we find in this paper.Comment: Revised version. A detailed discussion relating the power-law solutions with the linear K-essence field and inverse square potential, on one hand, and the models with divergent sound volocity, on the other, is adde

A general method for constructing essential uniform algebras

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an essential, natural counterexample to the peak point conjecture on each manifold-with-boundary of dimension at least three; and an essential, natural uniform algebra on the unit sphere in C3 containing the ball algebra and invariant under the action of the 3-torus. These examples show that a smoothness hypothesis in some results of Anderson and Izzo cannot be omitted

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

Tilted String Cosmologies

Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VI_h string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.Comment: 9 pages, Standard Latex Source. To appear in Physics Letters B Minor change: Authors now alphabetically liste