Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes

It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properties.Comment: 4 pages, some discussion and references are adde

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

A comparative study of verbal IQ, performance IQ and verbal IQ-performance IQ disparity among Turner syndrome patients and patients with primary amenorrhoea due to other aetiologies

Background: Assessing disparity in IQ is important in selecting an occupation and thus helping people lead a productive life. In Turner syndrome patients, this shall be more important as assessment of verbal IQ- and performance IQ disparity could be used in helping them select an occupation so that productivity and quality of life is not grossly compromised.Methods: Based on karyotyping, 30 patients with turner syndrome and 30 patients with primary amenorrhoea due to other aetiologies were selected for the study. Cytogenetic analysis was done for every case using G-banding technique. Assessment of intellectual functions was done using Wechsler Adult Intelligence Scale (WAIS).Results: Mean value of PIQ of X0 (turner) was 74.67 and that of XX (other amenorrhoea patients) was 90.30. Mean value of VIQ of X0 (turner) was 93.67 and that of XX (other amenorrhoea patients) was 93.60. Mean value of VIQ and PIQ disparity of X0 (turner) was 18.67 and that of XX (other amenorrhoea patients) was 3.Conclusions: Turner syndrome patients have high VIQ-PIQ disparity when compared to other primary amenorrhoea patients

Closed conformal Killing-Yano tensor and geodesic integrability

Assuming the existence of a single rank-2 closed conformal Killing-Yano tensor with a certain symmetry we show that there exist mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton-Jacobi equations.Comment: 17 pages, no figure, LaTe

X-ray bolometric corrections for Compton-thick active galactic nuclei

We present X-ray bolometric correction factors, $\kappa_{Bol}$ ($\equiv L_{Bol}/L_X$), for Compton-thick (CT) active galactic nuclei (AGN) with the aim of testing AGN torus models, probing orientation effects, and estimating the bolometric output of the most obscured AGN. We adopt bolometric luminosities, $L_{Bol}$, from literature infrared (IR) torus modeling and compile published intrinsic 2--10 keV X-ray luminosities, $L_{X}$, from X-ray torus modeling of NuSTAR data. Our sample consists of 10 local CT AGN where both of these estimates are available. We test for systematic differences in $\kappa_{Bol}$ values produced when using two widely used IR torus models and two widely used X-ray torus models, finding consistency within the uncertainties. We find that the mean $\kappa_{Bol}$ of our sample in the range $L_{Bol}\approx10^{42}-10^{45}$ erg/s is log$_{10}\kappa_{Bol}=1.44\pm0.12$ with an intrinsic scatter of $\sim0.2$ dex, and that our derived $\kappa_{Bol}$ values are consistent with previously established relationships between $\kappa_{Bol}$ and $L_{Bol}$ and $\kappa_{Bol}$ and Eddington ratio. We investigate if $\kappa_{Bol}$ is dependent on $N_H$ by comparing our results on CT AGN to published results on less-obscured AGN, finding no significant dependence. Since many of our sample are megamaser AGN, known to be viewed edge-on, and furthermore under the assumptions of AGN unification whereby unobscured AGN are viewed face-on, our result implies that the X-ray emitting corona is not strongly anisotropic. Finally, we present $\kappa_{Bol}$ values for CT AGN identified in X-ray surveys as a function of their observed $L_X$, where an estimate of their intrinsic $L_{X}$ is not available, and redshift, useful for estimating the bolometric output of the most obscured AGN across cosmic time.Comment: Accepted for publication in Ap

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte