Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.Comment: 17 pages, no figure

Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets

In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important non-trivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].Comment: 37 pages, no figure

Do Killing-Yano tensors form a Lie Algebra?

Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing-Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincare and (A)dS symmetry algebras.Comment: 17 page

3-quasi-Sasakian manifolds

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update

Conformal Yano-Killing tensor for the Kerr metric and conserved quantities

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed.Comment: 29 page

Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).Comment: 7 page

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

A gallotannin-rich fraction from Caesalpinia spinosa (Molina) Kuntze displays cytotoxic activity and raises sensitivity to doxorubicin in a leukemia cell line

<p>Abstract</p> <p>Background</p> <p>Enhancement of tumor cell sensitivity may help facilitate a reduction in drug dosage using conventional chemotherapies. Consequently, it is worthwhile to search for adjuvants with the potential of increasing chemotherapeutic drug effectiveness and improving patient quality of life. Natural products are a very good source of such adjuvants.</p> <p>Methods</p> <p>The biological activity of a fraction enriched in hydrolysable polyphenols (P2Et) obtained from <it>Caesalpinia spinosa </it>was evaluated using the hematopoietic cell line K562. This fraction was tested alone or in combination with the conventional chemotherapeutic drugs doxorubicin, vincristine, etoposide, camptothecin and taxol. The parameters evaluated were mitochondrial depolarization, caspase 3 activation, chromatin condensation and clonogenic activity.</p> <p>Results</p> <p>We found that the P2Et fraction induced mitochondrial depolarization, activated caspase 3, induced chromatin condensation and decreased the clonogenic capacity of the K562 cell line. When the P2Et fraction was used in combination with chemotherapeutic drugs at sub-lethal concentrations, a fourfold reduction in doxorubicin inhibitory concentration 50 (IC₅₀) was seen in the K562 cell line. This finding suggested that P2Et fraction activity is specific for the molecular target of doxorubicin.</p> <p>Conclusions</p> <p>Our results suggest that a natural fraction extracted from <it>Caesalpinia spinosa </it>in combination with conventional chemotherapy in combination with natural products on leukemia cells may increase therapeutic effectiveness in relation to leukemia.</p

A Target-Based High Throughput Screen Yields Trypanosoma brucei Hexokinase Small Molecule Inhibitors with Antiparasitic Activity

African sleeping sickness is a disease found in sub-Saharan Africa that is caused by the single-celled parasite Trypanosoma brucei. The drugs used widely now to treat infections are 50 years old and notable for their toxicity, emphasizing the need for development of new therapeutics. In the search for potential drug targets, researchers typically focus on enzymes or proteins that are essential to the survival of the infectious agent while being distinct enough from the host to avoid accidental targeting of the host enzyme. This work describes our research on one such trypanosome enzyme, hexokinase, which is a protein that the parasite requires to make energy. Here we describe the results of our search for inhibitors of the parasite enzyme. By screening 220,223 compounds for anti-hexokinase activity, we have identified new inhibitors of the parasite enzyme. Some of these are toxic to trypanosomes while having no effect on mammalian cells, suggesting that they may hold promise for the development of new anti-parasitic compounds