Quasinormal Modes of Charged Scalars around Dilaton Black Holes in 2+1 Dimensions: Exact Frequencies

We have studied the charged scalar perturbation around a dilaton black hole in 2 +1 dimensions. The wave equations of a massless charged scalar field is shown to be exactly solvable in terms of hypergeometric functions. The quasinormal frequencies are computed exactly. The relation between the quasinormal frequencies and the charge of the black hole, charge of the scalar and the temperature of the black hole are analyzed. The asymptotic form of the real part of the quasinormal frequencies are evaluated exactly.Comment: 20 pages and 7 figures, some references are added and some removed. There are some changes to the text. arXiv admin note: text overlap with arXiv:hep-th/040716

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

Proper Motions and CCD-photometry of Stars in the Region of the Open Cluster Trumpler 2

The results of the complex study of galactic open cluster Trumpler 2 are presented. In order to obtain the proper motions the positions of 2600 stars up to the limit magnitude B ~ 16.25 mag in the area 80x80 arcmin around the cluster were measured on 6 plates with the maximal epoch difference of 63 years. The root-mean error of the relative proper motions is 4.2 mas/yr. The catalogue of BV magnitudes of all the stars in the investigated area was compiled. Astrometric selection of the cluster members within the region of R<16 arcmin from the center of the cluster was made by means of the W.Sanders method. In that field 192 stars were found to have the individual membership probability greater then 85%, 148 of them are situated within the +/-3sigma_(B-V) band around the main sequence of the cluster. They are considered to be cluster members by two criteria. The U-B ~ B-V diagram plotted for the astrometrical cluster members by the data taken from the Washington catalogue of the UBV photometry in the galactic cluster fields (Hoag et al.1961) made it possible to redefine the value of the color excess E(B-V)=0.40 mag. The superposition of the MS of the cluster with the ZAMS Schmidt-Kaler leads to the coincidence at the value of the apparent distance module (V-Mv)=10.50 which corresponds to the distance r=725 pc. The luminosity and mass functions of the Trumpler 2 were constructed and the value of the slope Gamma=-1.90+/-0.22 was determined. The cluster age of 8.913x10^7 yr was determined. It is shown that the red giant on the late stage of the evolution (st N.1095) belongs to cluster and indicates the brightness variability. The possibility that the number of both known and recently discovered variables are cluster members was considered. Tables 2,3,3A,5 will be only available in the electronic form.Comment: 14 pages, 7 figure

Plane torsion waves in quadratic gravitational theories

The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the formula for commutator of the variation operator and Hodge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.Comment: 3 May 1998. - 11

Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators

It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These results imply that recent checks of the AdS/CFT correspondence actually test a nearly-BPS sector.Comment: 12 pages, no figures; v2: new section on CFT operators and new references added, discussion section and acknowledgements modified, abstract rephrashe

A note on spin chain/string duality

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.Comment: v.2 One reference added, typos corrected, 21 page