Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all dimensions, if one specialises the rotation parameters so that the metrics have cohomogeneity 2. Furthermore, we show that this property of separability extends to the NUT generalisations of these cohomogeneity-2 black holes that we obtained in a recent paper. In all these cases, we also construct the associated irreducible rank-2 Killing tensor whose existence reflects the hidden symmetry that leads to the separability. We also consider some cohomogeneity-1 specialisations of the new Kerr-NUT-AdS metrics, showing how they relate to previous results in the literature.Comment: Latex, 15 pages, minor typos correcte

Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes

We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.Comment: 4 pages, no figure

Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions

We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Myers-Perry black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters, which significantly enlarges the rotational symmetry group. We explicitly construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.Comment: 16 pages, LaTeX2

A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable.Comment: LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference added, introduction expanded, published versio

Studies on influence of modified atmospheric storage conditions on biochemical parameters in pigeonpea seeds

An experiment was conducted to study the influence of modified atmospheric storage conditions on biochemical parameters of pigeonpea seeds. The experiment was conducted at the Department of Seed Science and Technology, College of Agriculture, Raichur, Karnataka. The seeds are exposed to various gaseous combinationsand stored in 700 gauge polyethylene bag for ten months during July-2012 to April- 2013. The results revealed that, the seeds exposed to gaseous combination of 40% N2+00% O2+ 60% CO2 showed less reduction in dehydrogenase enzyme activity and protein content (0.276 OD (optical density) value, 19.33 % respectively) as compared to the control (0.211 OD value and 18.13 % respectively) after ten months of storage. In addition less seed leachate (2.029 dSm-1) was recorded in gaseous combination of 40% N2+00% O2+ 60% CO2 as compared to control (2.207dSm-1). It indicates the potential use of modified atmospheric storage technology for maintenance of seed viability and vigour during storage in pulses

Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.Comment: 4 pages. We have now found that the geodesic motion is not just integrable, but completely integrabl

Abscisic acid induced seed dormancy and climate resilience in fox tail millet (Setaria italica L.) genotypes

A laboratory experiment was conducted at Department of Seed Science and Technology, UAS Raichur to estimate ABA content in foxtail millet (Setaria italica L.) using Phytodetek ABA Test Kit. ABA estimation in millets is helpful to trace out the reason behind the dormancy in millets and is less explored. Nine genotypes were studied in the present investigation. Among the foxtail millet genotypes, the highest dormancy duration of 35 days was observed in two genotypes viz., DHFt-4-5 and DHFt-5-3 and slight dormancy was noticed in the genotype DHFt- 35-1. The genotype DHFt-35-1 recorded lowest ABA concentration of 3.199 pmol/g f. w. followed by genotypes DHFt-2-5 and DHFt-2-5-1 (3.266 and 3.291 pmol/g f. w. respectively). Highest ABA concentration was found in DHFt-5-3 (3.404 pmol/g f. w.) followed by DHFt-4-5 (3.396 pmol/g f. w.). Thus it was concluded that ABA in millet seeds makes them ‘climate smart crops’ and during the climate change regime, it is only millets that can ensure India’s food and nutrition needs in future

Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes

In [arXiv:hep-th/0611083] we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [arXiv:hep-th/0612029] is also briefly discussed.Comment: 8 pages, no figure

Seed polymer coating with Zn and Fe nanoparticles: An innovative seed quality enhancement technique in pigeonpea

A laboratory study was undertaken to know the effect of seed polymer coating with Zn and Fe nanoparticles (NPs) at different concentration (10, 25, 50, 100, 250, 500, 750 and 1000 ppm) in pigeonpea at Department of Seed Science and Technology, UAS, Raichur. Among the treatments seed polymer coating with Zn NPs at 750 ppm recorded significantly higher seed germination (96.00 %), seedling length (26.63 cm), seedling dry weight (85.00 mg), speed of germination (32.95), field emergence (89.67 %), seedling vigour index (2556), dehydrogenase activity (0.975 OD value) and ?-amylase activity (25.67 mm) and lowest abnormal seedlings (2.50 %) over their bulk forms and control followed by Fe and Zn NPs at 500 ppm. However, in contrast to beneficial effects, these NPs also shown inhibitory effect on germination and seedling growth at higher concentration (nano Zn >750 ppm and nano Fe > 500 ppm). Hence, from the results it is concluded that Zn NPs at 750 ppm can be used to enhance quality of the pigeonpea seeds

Biochemical investigations on vigour enhancement in aged seeds upon seed priming in onion

Loss in seed quality that occurs during all process, from maturation in the field to storage, leads to seed deterioration. Storage of onion seeds under ambient, hot and humid conditions is very problematic since these conditions deteriorate seed quality faster. Seed deterioration is associated with many metabolic defects that occur due to changes in enzymes and protein levels. This deterioration can be rectified to the extent possible by the technique of seed priming. The results clearly indicated that priming will restore the lost seed vigour in aged seeds due to reactivation of enzyme activity in old seeds. The germination percentage improved from 60% to 79.5% and 72.5% in GA3 and hydroprimed, respectively. Priming will also restore the lost seed vigour in aged seeds due to reactivation of proteins in old seeds and expression of these proteins in priming treatments are related to priming induced proteins in contrast to their absence in the aged seeds which are necessary for germination and longevity of seeds