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.

A Quantitative Method for the Study of Pollen and Spores in Bog Sediments

A filtration method involving a membrane filter for the collection and subsequent microscopic examination of weighed, treated samples is presented. The filter and the sample collected upon it are both mounted for microscopic examination. The filter permits sufficient light passage for identification of spores and pollen upon its surface. This method permits a more accurate transfer of weighed samples from centrifuge tubes to microscope slides

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

Changes in monkey crystalline lens spherical aberration during simulated accommodation in a lens stretcher

8 págs.; 7 figs.; 2 apps.© 2015 The Association for Research in Vision and Ophthalmology, Inc. PURPOSE. The purpose of this study was to quantify accommodation-induced changes in the spherical aberration of cynomolgus monkey lenses. METHODS. Twenty-four lenses from 20 cynomolgus monkeys (Macaca fascicularis; 4.4-16.0 years of age; postmortem time 13.5±13.0 hours) were mounted in a lens stretcher. Lens spherical aberration was measured in the unstretched (accommodated) and stretched (relaxed) states with a laser ray tracing system that delivered 51 equally spaced parallel rays along 1 meridian of the lens over the central 6-mm optical zone. A camera mounted below the lens was used to measure the ray height at multiple positions along the optical axis. For each entrance ray, the change in ray height with axial position was fitted with a third-order polynomial. The effective paraxial focal length and Zernike spherical aberration coefficients corresponding to a 6-mm pupil diameter were extracted from the fitted values. RESULTS. The unstretched lens power decreased with age from 59.3±6 4.0 diopters (D) for young lenses to 45.7±6 3.1 D for older lenses. The unstretched lens shifted toward less negative spherical aberration with age, from -6.3±0.7 lm for young lenses to-5.0±0.5 lm for older lenses. The power and spherical aberration of lenses in the stretched state were independent of age, with values of 33.5±6 3.4 D and-2.6±0.5 lm, respectively. CONCLUSIONS. Spherical aberration is negative in cynomolgus monkey lenses and becomes more negative with accommodation. These results are in good agreement with the predicted values using computational ray tracing in a lens model with a reconstructed gradient refractive index. The spherical aberration of the unstretched lens becomes less negative with age.Supported by National Institutes of Health Grants R01EY14225, R01EY021834, and F31EY021444 Ruth L. Kirschstein National Research Service Award individual predoctoral fellowship [BM]), and center Grant P30EY14801; Australian government Cooperative Research Centre Scheme (Vision CRC); Florida Lions Eye Bank; Karl R. Olsen and Martha E. Hildebrandt; an unrestricted grant from Research to Prevent Blindness; Henri and Flore Lesieur Foundation (JMP); Spanish government Grant FIS2011-25637; and European Research Council Grants ERC-2011-AdG-294099 and CSIC i-LINKþ0609Peer Reviewe

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

Type II Einstein spacetimes in higher dimensions

This short note shows that many of the results derived by Pravda et al (Class. Quant. Grav. 24 4407-4428) for higher-dimensional Type D Einstein spacetimes can be generalized to all Einstein spacetimes admitting a multiple WAND; the main new result being the extension to include the Type II case. Examples of Type D Einstein spacetimes admitting non-geodesic multiple WANDs are given in all dimensions greater than 4.Comment: 10 pages. v2: Various minor corrections and clarifications. Accepted by Class. Quantum Gra

Ultraspinning instability: the missing link

We study linearized perturbations of Myers-Perry black holes in d=7, with two of the three angular momenta set to be equal, and show that instabilities always appear before extremality. Analogous results are expected for all higher odd d. We determine numerically the stationary perturbations that mark the onset of instability for the modes that preserve the isometries of the background. The onset is continuously connected between the previously studied sectors of solutions with a single angular momentum and solutions with all angular momenta equal. This shows that the near-extremality instabilities are of the same nature as the ultraspinning instability of d>5 singly-spinning solutions, for which the angular momentum is unbounded. Our results raise the question of whether there are any extremal Myers-Perry black holes which are stable in d>5.Comment: 19 pages. 1 figur

Morphology, Ultrastructure, and Function of Extrafloral Nectaries in Three Species of Caesalpiniaceae

Light and electron microscopy reveal that the morphologically well-differentiated petiolar nectaries of Chamaecrista fasciculata, Senna hepecarpa, and S. marilandica have an unusually simple anatomy consisting of an epidermis immediately subtended by a mass of small, loosely-packed parenchyma cells. Vascular strands from the petiolar bundles enter the nectary and terminate as phloem within or near this parenchyma. In mature, secreting nectaries, the cuticle of the epidermis extends between the epidermal cells and into the nectary parenchyma, where it occupies, but does not occlude, much of the free space of this tissue. The cutin is not found below the level of the phloem endings and is not found in very young nectaries, but begins to appear when cell expansion occurs. These observations, together with the proximity of phloem to the parenchyma free space and the almost exclusive presence of sucrose in the nectar suggest that, although symplastic transport of sugars may occur, an alternate pathway for secretion is possible whereby sugar diffuses from the phloem, moves through the nectary to the surface without being acted upon by cells in transit, and is released by rupture of the external cuticle and the concomitant activity of foraging ants and other nectar feeders

Combined anterior segment OCT and wavefront-based autorefractor using a shared beam

We have combined an anterior segment (AS) optical coherence tomography (OCT) system and a wavefront-based aberrometer with an approach that senses ocular wavefront aberrations using the OCT beam. Temporal interlacing of the OCT and aberrometer channels allows for OCT images and refractive error measurements to be acquired continuously and in real-time. The system measures refractive error with accuracy and precision comparable to that of clinical autorefractors. The proposed approach provides a compact modular design that is suitable for integrating OCT and wavefront-based autorefraction within the optical head of the ophthalmic surgical microscope for guiding cataract surgery or table-top devices for simultaneous autorefraction and ocular biometry

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio