Applications of hidden symmetries to black hole physics

This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference (June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan

Predicting Potential Distribution of Orchis Galilaea in Lebanon Using GIS

Orchis galilaea is the only Lebanese orchid that is restricted geographically to Lebanon, Palestine and Jordan. It is a terrestrial orchid that attracts its pollinator by sexual deception while offering no reward. The full distribution of this orchid in Lebanon has not been determined. This study is part of ongoing research into the population dynamics of the orchid to form a management plan for its conservation. A Geographic Information System (GIS) was used to identify the habitat characteristics of O. galilaea and map its distribution in Lebanon by combining known locations with digital layers of environmental variables, including topography, land cover, soil type, geology and precipitation. Classes within each environmental parameter were defined and weighted according to their frequency of occurrence at extant sites. A predictive GIS model was developed by overlaying the five layers of the habitat characteristics. The predicted distribution map of O. galilaea was then validated by confirming presence of the orchid in the predicted locations and absence in the unsuitable areas through exploration field trips. Eighty five locations were surveyed and seven previously unknown populations of O. galilaea were discovered. These new O. galilaea locations were all correctly predicted by the model as potential habitat. The accuracy of the model was confirmed as it was significantly more likely to find the orchid in predicted suitable habitat compared with unsuitable habitat. Combining ecological habitat characteristics using GIS proved to be a useful tool to successfully predict the potential distribution of O. galilaea in Lebanon and will assist in planning its conservation measures

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

Color Glass Condensate in Brane Models or Don't Ultra High Energy Cosmic Rays Probe 1015eV10^{15}eV Scale ?

In a previous work hep-ph/0203165 we have studied propagation of relativistic particles in the bulk for some of most popular brane models. Constraints have been put on the parameter space of these models by calculating the time delay due to propagation in the bulk of particles created during the interaction of Ultra High Energy Cosmic Rays with protons in the terrestrial atmosphere. The question was however raised that probability of hard processes in which bulk modes can be produced is small and consequently, the tiny flux of UHECRs can not constrain brane models. Here we use Color Glass Condensate (CGC) model to show that effects of extra dimensions are visible not only in hard processes when the incoming particle hits a massive Kaluza-Klein mode but also through the modification of soft/semi-hard parton distribution. At classical level, for an observer in the CM frame of UHECR and atmospheric hadrons, color charge sources are contracted to a thin sheet with a width inversely proportional to the energy of the ultra energetic cosmic ray hadron and consequently they can see an extra dimension with comparable size. Due to QCD interaction a short life swarm of partons is produced in front of the sheet and its partons can penetrate to the extra-dimension bulk. This reduces the effective density of partons on the brane or in a classical view creates a delay in the arrival of the most energetic particles if they are reflected back due to the warping of the bulk. In CGC approximation the density of swarm at different distance from the classical sheet can be related and therefore it is possible (at least formally) to determine the relative fraction of partons in the bulk and on the brane at different scales. Results of this work are also relevant to the test of brane models in hadron colliders like LHC.Comment: 17 pages, 3 figures. Text is modified to highlight the relation between the distribution gluons at high and low rapidity scales. v3: published versio

Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing-Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong-Cvetic-Lu-Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.Comment: Dedicated to Nihat Berker on the occasion of his 60th birthday; 13 pages, REVTe

Kerr-NUT-de Sitter Curvature in All Dimensions

We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the Kerr-NUT-de Sitter metric is clarified for all dimensions. It is shown that the metrics are of type D.Comment: 10 page

Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes

We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p mutually commuting Killing vectors it is possible to introduce a concept of a $\xi$-brane, that is a p-brane with the worldvolume generated by these fields and a 1-dimensional curve. We discuss integrability of such $\xi$-branes in the Kerr-NUT-(A)dS spacetime.Comment: 8 pages, no figure

Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a non-degenerate CKY tensor.Comment: 24 pages, LaTeX; v2: references added, published versio

Multicentre evaluation of the Naída Ci Q70 sound processor: Feedback from cochlear implant users and professionals

The aim of this survey was to gather data from both implant recipients and professionals on the ease of use of the Naída CI Q70 (Naída CI) sound processor from Advanced Bionics and on the usefulness of the new functions and features available. A secondary objective was to investigate fitting practices with the new processor. A comprehensive user satisfaction survey was conducted in a total of 186 subjects from 24 centres. In parallel, 23 professional questionnaires were collected from 11 centres. Overall, there was high satisfaction with the Naída CI processor from adults, children, experienced and new CI users as well as from professionals. The Naída CI processor was shown as being easy to use by all ages of recipients and by professionals. The majority of experienced CI users rated the Naída CI processor as being similar or better than their previous processor in all areas surveyed. The Naída CI was recommended by the professionals for fitting in all populations. Features like UltraZoom, ZoomControl and DuoPhone would not be fitted to very young children in contrast to adults. Positive ratings were obtained for ease of use, comfort and usefulness of the new functions and features of the Naída CI sound processor. Seventy-seven percent of the experienced CI users rated the new processor as being better than their previous sound processor from a general point of view. The survey also showed that fitting practices were influenced by the age of the user

Hidden Symmetries and Black Holes

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.Comment: 13 pages, 3 figures. To appear in the proceedings of the NEB-13 conferenc