Generalized hidden symmetries and the Kerr-Sen black hole

We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their relationship to Killing tensors and the separability of various field equations. We further demonstrate that the Kerr-Sen black hole spacetime of heterotic string theory, as well as its generalization to all dimensions, possesses a generalized closed conformal Killing-Yano 2-form with respect to a torsion identified with the 3-form occuring naturally in the theory. Such a 2-form is responsible for complete integrability of geodesic motion as well as for separability of the scalar and Dirac equations in these spacetimes.Comment: 33 pages, no figure

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

A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra

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

Symmetries of the Dirac operator with skew-symmetric torsion

In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise to symmetries of the Dirac operator in the case of strong Kahler with torsion (KT) and strong hyper-Kahler with torsion (HKT) manifolds

Some Spacetimes with Higher Rank Killing-Stackel Tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime

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