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

Neuroadaptations in the Cellular and Postsynaptic Group 1 Metabotropic Glutamate Receptor mGluR5 and Homer Proteins Following Extinction of Cocaine Self-administration

This study examined the role of group1 metabotropic glutamate receptor mGluR5 and associated postsynaptic scaffolding protein Homer1b/c in behavioral plasticity after three withdrawal treatments from cocaine self-administration. Rats self-administered cocaine or saline for 14 days followed by a withdrawal period during which rats underwent extinction training, remained in their home cages, orwere placed in the self-administration chambers in the absence of extinction. Subsequently, the tissue level and distribution of proteins in the synaptosomal fraction associated with the postsynaptic densitywere examined. Cocaine self-administration followed by home cage exposure reduced the mGluR5 protein in nucleus accumbens (NA) shell and dorsolateral striatum. While extinction training reduced mGluR5 protein in NAshell, NAcore and dorsolateral striatum did not display any change. The scaffolding protein PSD95 increased in NAcore of the extinguished animals. Extinction of drug seeking was associated with a significant decrease in the synaptosomal mGluR5 protein in NAshell and an increase in dorsolateral striatum, while that of NAcore was not modified. Interestingly, both Homer1b/c and PSD95 scaffolding proteins were decreased in the synaptosomal fraction after extinction training in NAshell but not NAcore. Extinguished drug-seeking behavior was also associated with an increase in the synaptosomal actin proteins in dorsolateral striatum. Therefore, extinction of cocaine seeking is associated with neuroadaptations in mGluR5 expression and distribution that are region-specific and consist of extinction-induced reversal of cocaine-induced adaptations aswell as emergent extinction-induced alterations. Concurrent plasticity in the scaffolding proteins further suggests that mGluR5 receptor neuroadaptations may have implications for synaptic function

Synthesis, Crystal Structure and Photophysical Properties of Lanthanide Coordination Polymers of 4- 4-(9H-Carbazol-9-Yl)Butoxy Benzoate: The Effect of Bidentate Nitrogen Donors on Luminescence

A new aromatic carboxylate ligand, 4-[4-(9H-carbazol-9-yl)butoxy]benzoic acid (HL), has been synthesized by the replacement of the hydroxyl hydrogen of 4-hydroxy benzoic acid with a 9-butyl-9H-carbazole moiety. The anion derived from HL has been used for the support of a series of lanthanide coordination compounds [Ln = Eu (1), Gd (2) and Tb (3)]. The new lanthanide complexes have been characterized by a variety of spectroscopic techniques. Complex 3 was structurally authenticated by single-crystal X-ray diffraction and found to exist as a solvent-free 1D coordination polymer with the formula [Tb(L)(3)](n). The structural data reveal that the terbium atoms in compound 3 reside in an octahedral ligand environment that is somewhat unusual for a lanthanide. It is interesting to note that each carboxylate group exhibits only a bridging-bidentate mode, with a complete lack of more complex connectivities that are commonly observed for extended lanthanide-containing solid-state structures. Examination of the packing diagram for 3 revealed the existence of two-dimensional molecular arrays held together by means of CH-pi interactions. Aromatic carboxylates of the lanthanides are known to exhibit highly efficient luminescence, thus offering the promise of applicability as optical devices. However, due to difficulties that arise on account of their polymeric nature, their practical application is somewhat limited. Accordingly, synthetic routes to discrete molecular species are highly desirable. For this purpose, a series of ternary lanthanide complexes was designed, synthesized and characterized, namely [Eu(L)(3)(phen)] (4), [Eu(L)(3)(tmphen)] (5), [Tb(L)(3)(phen)] (6) and [Tb(L)(3)(tmphen)] (7) (phen = 1,10-phenanthroline and tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline). The photophysical properties of the foregoing complexes in the solid state at room temperature have been investigated. The quantum yields of the ternary complexes 4 (9.65%), 5 (21.00%), 6 (14.07%) and 7 (32.42%), were found to be significantly enhanced in the presence of bidentate nitrogen donors when compared with those of the corresponding binary compounds 1 (0.11%) and 3 (1.45%). Presumably this is due to effective energy transfer from the ancillary ligands.Council of Scientific and Industrial Research (CSIR-TAPSUN Project) SSL, NWP-55CSIR, New DelhiRobert A. Welch Foundation F-0003Chemistr

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