Marine stratocumulus cloud characteristics from multichannel satellite measurements

Understanding the effects of aerosols on the microphysical characteristics of marine stratocumulus clouds, and the resulting influence on cloud radiative properties, is a primary goal of FIRE. The potential for observing variations of cloud characteristics that might be related to variations of available aerosols is studied. Some results from theoretical estimates of cloud reflectance are presented. Also presented are the results of comparisons between aircraft measured microphysical characteristics and satellite detected radiative properties of marine stratocumulus clouds. These results are extracted from Mineart where the analysis procedures and a full discussion of the observations are presented. Only a brief description of the procedures and the composite results are presented

On the structure of the ergosurface of Pomeransky-Senkov black rings

We study the properties of the ergosurface of the Pomeransky-Senkov black rings, and show that it splits into an "inner"' and an "outer" region. As for the singular set, the topology of the "outer ergosurface" depends upon the value of parameters.Comment: 14 pages, 1 figur

Perturbations of higher-dimensional spacetimes

We discuss linearized gravitational perturbations of higher dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher dimensional generalizations of the 4d Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.Comment: 21 pages (v2:Minor corrections, accepted by CQG.

Generalization of the Geroch-Held-Penrose formalism to higher dimensions

Geroch, Held and Penrose invented a formalism for studying spacetimes admitting one or two preferred null directions. This approach is very useful for studying algebraically special spacetimes and their perturbations. In the present paper, the formalism is generalized to higher-dimensional spacetimes. This new formalism leads to equations that are considerably simpler than those of the higher-dimensional Newman-Penrose formalism employed previously. The dynamics of p-form test fields is analyzed using the new formalism and some results concerning algebraically special p-form fields are proved.Comment: 24 page

Algebraic classification of five-dimensional spacetimes using scalar invariants

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of a particular algebraic type. We demonstrate the discriminant approach by applying the techniques to the Sorkin-Gross-Perry soliton, the supersymmetric and doubly-spinning black rings and some other higher dimensional spacetimes. We show that even in the case of some very complicated metrics it is possible to compute the relevant discriminants and extract useful information from them

A new special class of Petrov type D vacuum space-times in dimension five

Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type $D$ vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl alligned null directionsComment: 4 pages, 1 table, no figures. Contribution to the proceedings of the Spanish Relativity Meeting 2010 held in Granada (Spain

Formal Reasoning Using an Iterative Approach with an Integrated Web IDE

This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE designed for the purpose. Our experience in using such an IDE, supported by a 'push-button' verifying compiler in a classroom setting, reveals the highly iterative process learners use to arrive at suitably specified, automatically provable code. We explain how the IDE facilitates reasoning at each step of this process by providing human readable verification conditions (VCs) and feedback from an integrated prover that clearly indicates unprovable VCs to help identify obstacles to completing proofs. The paper discusses the IDE's usage in verified software development using several examples drawn from actual classroom lectures and student assignments to illustrate principles of design-by-contract and the iterative process of creating and subsequently refining assertions, such as loop invariants in object-based code.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338

Type III and N Einstein spacetimes in higher dimensions: general properties

The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n-dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding (possibly twisting) solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behaviour of the Weyl "physical" components for large values of r, and thus to discuss, e.g., how the presence of twist affects polarization modes, and qualitative differences between four and higher dimensions. Further, the r-dependence of certain non-zero scalar curvature invariants of expanding spacetimes is used to demonstrate that curvature singularities may generically be present. As an illustration, several explicit type N/III spacetimes that solve Einstein's vacuum equations (with a possible cosmological constant) in higher dimensions are finally presented.Comment: 19 page

Spinor classification of the Weyl tensor in five dimensions

We investigate the spinor classification of the Weyl tensor in five dimensions due to De Smet. We show that a previously overlooked reality condition reduces the number of possible types in the classification. We classify all vacuum solutions belonging to the most special algebraic type. The connection between this spinor and the tensor classification due to Coley, Milson, Pravda and Pravdov\'a is investigated and the relation between most of the types in each of the classifications is given. We show that the black ring is algebraically general in the spinor classification.Comment: 40 page

Kerr-Schild spacetimes with (A)dS background

General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with non-expanding k are shown to be of Weyl type N, while the expanding spacetimes are of type II or D. It is shown that this class of spacetimes obeys the optical constraint. This allows us to solve Sachs equation, determine r-dependence of boost weight zero components of the Weyl tensor and discuss curvature singularities.Comment: 17 pages, minor change