Geometric properties of generalized symmetric spaces

It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized symmetric spaces

Turbulent dissipation in the interstellar medium: implications for galaxy formation and evolution

We study turbulent dissipation in the ISM and explore some implications for galaxy formation and evolution using 2D MHD numerical simulations of compressible fluids. The turbulent kinetic energy E_k is injected by stellar sources formed self-consistently in the simulation. In the ISM-like fluid, regimes of both forced and decaying turbulence coexist. In the active turbulent regions (forced regime), E_k is dissipated locally and efficiently. In the decaying regime (far from input sources), E_k(t) decays ~(1+t)^-0.8. The residual turbulent motions may propagate distances of the order of the observed disk height, suggesting that turbulence may be the responsible of vertical support and star formation self-regulation at the disk level, but not at the level of the whole cosmological halo, as would be required in some models of galaxy formation.Comment: 3 pages, uses rmaa.cls, to appear in "Astrophysical Plasmas: Codes, Models, and Observations", Eds. J. Franco, J. Arthur, N. Brickhouse, Rev.Mex.AA Conf. Series. An error in the calculation of the dissipation time, t_d, was corrected (it referred to the dissipation in the forced regions). Now we report the global t_d, which is the relevant quantity for the whole flo

Applying a one-dimensional PDR model to the Taurus molecular cloud and its atomic envelope

In this contribution, we test our previously published one-dimensional PDR model for deriving total hydrogen volume densities from HI column density measurements in extragalactic regions by applying it to the Taurus molecular cloud, where its predictions can be compared to available data. Also, we make the first direct detailed comparison of our model to CO(1-0) and far-infrared emission. Using an incident UV flux G0 of 4.25 ({\chi} = 5) throughout the main body of the cloud, we derive total hydrogen volume densities of \approx 430 cm-3, consistent with the extensive literature available on Taurus. The distribution of the volume densities shows a log-normal shape with a hint of a power-law shape on the high density end. We convert our volume densities to H2 column densities assuming a cloud depth of 5 parsec and compare these column densities to observed CO emission. We find a slope equivalent to a CO conversion factor relation that is on the low end of reported values for this factor in the literature (0.9 x 1020 cm-2 (K km s-1)-1), although this value is directly proportional to our assumed value of G0 as well as the cloud depth. We seem to under-predict the total hydrogen gas as compared to 100 {\mu}m dust emission, which we speculate may be caused by a higher actual G0 incident on the Taurus cloud than is generally assumed.Comment: 14 pages, 14 figures. Accepted for publication in MNRA

Strong Field Gravitational Lensing by a Kerr Black Hole

We consider a Kerr black hole acting as a gravitational deflector within the geometrical optics, and point source approximations. The Kerr black hole gravitational lens geometry consisting of an observer and a source located far away and placed at arbitrary inclinations with respect to the black hole's equatorial plane is studied in the strong field regime. For this geometry the null geodesics equations of our interest can go around the black hole several times before reaching the observer. Such photon trajectories are written in terms of the angular positions in the observer's sky and therefore become "lens equations". As a consequence, we found for any image a simple classification scheme based in two integers numbers: the number of turning points in the polar coordinate $\theta$, and the number of windings around the black hole's rotation axis. As an application, and to make contact with the literature, we consider a supermassive Kerr black hole at the Galactic center as a gravitational deflector. In this case, we show that our proposed computational scheme works successfully by computing the positions and magnifications of the relativistic images for different source-observer geometries. In fact, it is shown that our general procedure and results for the positions and magnifications of the images off the black hole's equatorial plane, reduce and agree with well known cases found in the literature.Comment: ReVTeX, 19 pages, 10 figures and 7 tables. Final version with some grammatical changes to abstract and text (equations left unchanged). Submitted to PR

Radiodetection of neutrino interactions in ice

We study the Cherenkov radiopulses emitted in PeV and EeV neutrino interactions in ice. We discuss how the rich radiation pattern in the 100 MHz to 1 GHz frequency range, in principle allows the measurement of shower elongation produced in neutrino interactions opening up the possibility of flavor recognition identifying charged current electron neutrino interactions.Comment: 4 pages, 2 ps figures, to be published in the proceedings of 26th International Cosmic Ray Conference (Salt Lake City, 1999

Inflationary Cosmology: From Theory to Observations

The main aim of this paper is to provide a qualitative introduction to the cosmic inflation and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problems that challenge the Standard Big Bang cosmology i.e. Flatness, Horizon and Monopole problem, and additionally provides an explanation for the initial conditions observed throughout the Large-Scale Structure of the Universe, such as galaxies. In this review we describe the general solutions carry out by a single scalar field. Then with the use of current surveys, we show the constraints imposed on the inflationary parameters $(n_{\rm s},r)$ which allow us to make the connection between theoretical and observational cosmology. In this way, with the latest results, it is possible to choose or at least to constrain the right inflationary model, parameterised by a single scalar field potential $V(\phi)$.Comment: Lecture Notes in Cosmology. 37 pages, 15 figures, 2 table

Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons

The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface with a metric of constant Gauss curvature form one family; there are, however, two other families. For a surface in one of these other two families, we examine the Lie algebra of affine Killing vector fields and we give a complete classification of the homogeneous affine gradient Ricci solitons. The rank of the Ricci tensor plays a central role in our analysis

Conformal geometry of non-reductive four-dimensional homogeneous spaces

We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.Comment: New version correcting some inaccuracies in the original pape

Half conformally flat gradient Ricci almost solitons

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a steady traceless $\kappa$-Einstein soliton and is realized on the cotangent bundle of an affine surface

Digraphs with at most one trivial critical ideal

Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one.Comment: 12 pages, 4 figure