Godel-Type Metrics in Various Dimensions

Godel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D-1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Einstein-Maxwell field equations with a dust distribution in D dimensions. The only essential field equation in the procedure turns out to be the source-free Maxwell's equation in the relevant background. Similarly the geodesics of this type of metric are described by the Lorentz force equation for a charged particle in the lower dimensional geometry. It is explicitly shown with several examples that Godel-type metrics can be used in obtaining exact solutions to various supergravity theories and in constructing spacetimes that contain both closed timelike and closed null curves and that contain neither of these. Among the solutions that can be established using non-flat backgrounds, such as the Tangherlini metrics in (D-1)-dimensions, there exists a class which can be interpreted as describing black-hole-type objects in a Godel-like universe.Comment: REVTeX4, 19 pp., no figures, improved and shortened version, note the slight change in the title [accepted for publication in Classical and Quantum Gravity

Exact static solutions in four dimensional Einstein-Maxwell-Dilaton gravity

Classes of exact static solutions in four-dimensional Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It's shown that spherically symmetric solutions, except the case of charged dilaton black hole, represent globally naked strong curvature singularities.Comment: 8 pages, late

On a particular type of product manifolds and shear-free cosmological models

Cataloged from PDF version of article.Shear-free flows or observer fields are important objects of study in general relativity; stationary or rigid observers are important examples of shear-free reference frames. In this paper, we introduce a geometric structure based on a local coordinate expression of metrics admitting a shear-free reference frame. Furthermore, we investigate a large sub-class of these models ('tilted' warped products) that includes the Robertson-Walker spacetime, the Gödel spacetime and other models of Gödel type. We present a novel example of a rotating and expanding cosmological model that is contained in this class. Finally, we describe the geodesic barotropic perfect fluid solutions. © 2011 IOP Publishing Ltd

Degenerate Svinolupov KdV systems

We find infinitely many coupled systems of KdV type equations which are integrable. We give also their recursion operators

The effect of different packaging materials on proteolysis, sensory scores and gross composition of tulum cheese

In this study, tulum cheese was manufactured using raw ewe’s milk and was ripened in goat’s skin and plastic bags. The effect of ripening materials (skin bag or plastic) on proteolysis was investigated during 120 days of ripening. In addition, sensory scores of the cheeses were assessed at the 90th and 120th days. The gross composition was also determined at the initial stage of ripening. The results showed that, some significant differences were noted between cheeses ripened in goat’s skin and plastic bags in terms of gross composition due to the porous structure of skin bag, which causes moisture loses during ripening. Significant differences were observed in proteolysis indices including water, 12% tricholoroacetic acid and 5% phosphotungstic acid-soluble nitrogen fractions among the cheese samples during ripening. Proteolysis levels were higher in tulum cheeses ripened in goat’s skin.Key words: Tulum cheese, packaging material, sensory analysis, ripening, proteolysis

Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations

Cataloged from PDF version of article.Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in ℝ3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg-de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity. © 2000 American Institute of Physics

Closed timelike curves and geodesics of Godel-type metrics

it is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower-dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed

Type IIB Colliding Plane Waves

Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in $2n+2$--dimensional Einstein gravity with a $n+1$-form flux. By using an isomorphism with the four-dimensional problem, we construct exact solutions analogous to the Szekeres vacuum solution in four dimensions. The higher-dimensional versions of the Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively in the vicinity of the light-cone. We find that under small perturbations, a curvature singularity is generically produced, leading to both space-like and time-like singularities. For $n=4$, our results pertain to the collision of two ten-dimensional type IIB Blau - Figueroa o'Farrill - Hull - Papadopoulos plane waves.Comment: 20+10 pages, 2 figures, uses JHEP3.cls; v2: refs [3,10,22] corrected, remark added below (3.9) on inexistence of conformally flat CPW in our ansatz, final version to appear in JHE