A new form of the rotating C-metric

In a previous paper, we showed that the traditional form of the charged C-metric can be transformed, by a change of coordinates, into one with an explicitly factorizable structure function. This new form of the C-metric has the advantage that its properties become much simpler to analyze. In this paper, we propose an analogous new form for the rotating charged C-metric, with structure function G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where r_\pm are the usual locations of the horizons in the Kerr-Newman black hole. Unlike the non-rotating case, this new form is not related to the traditional one by a coordinate transformation. We show that the physical distinction between these two forms of the rotating C-metric lies in the nature of the conical singularities causing the black holes to accelerate apart: the new form is free of torsion singularities and therefore does not contain any closed timelike curves. We claim that this new form should be considered the natural generalization of the C-metric with rotation.Comment: 13 pages, LaTe

Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.Comment: 12 pages, 5 figure

Palladium-Catalyzed Oxidation of β-C(sp3)-H Bonds of Primary Alkylamines through a Rare Four-Membered Palladacycle Intermediate.

Site-selective functionalizations of C-H bonds are often achieved with a directing group that leads to five- or six-membered metallacyclic intermediates. Analogous reactions that occur through four-membered metallacycles are rare. We report a challenging palladium-catalyzed oxidation of primary C-H bonds β to nitrogen in an imine of an aliphatic amine, a process that occurs through a four-membered palladacyclc intermediate. The success of the reaction relies on the identification, by H/D exchange, of a simple directing group (salicylaldehyde) capable of inducing the formation of this small ring. To gain insight into the steps of the catalytic cycle of this unusual oxidation reaction, a series of mechanistic experiments and density functional theory (DFT) calculations were conducted. The experimental studies showed that cleavage of the C-H bond is rate-limiting and formation of the strained four-membered palladacycle is thermodynamically uphill. DFT calculations corroborated these conclusions and suggested that the presence of an intramolecular hydrogen bond between the oxygen of the directing group and hydroxyl group of the ligating acetic acid is crucial for stabilization of the palladacyclic intermediate

Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis

We express the complex potential E and the metrical fields omega and gamma of all stationary axisymmetric vacuum spacetimes that result from the application of two successive quadruple-Neugebauer (or two double-Harrison) transformations to Minkowski space in terms of data specified on the symmetry axis, which are in turn easily expressed in terms of multipole moments. Moreover, we suggest how, in future papers, we shall apply our approach to do the same thing for those vacuum solutions that arise from the application of more than two successive transformations, and for those electrovac solutions that have axis data similar to that of the vacuum solutions of the Neugebauer family. (References revised following response from referee.)Comment: 18 pages (REVTEX

Generating anisotropic fluids from vacuum Ernst equations

Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy-momentum tensor and with the equation of state compatible with the field equations. The method is presented by using different coordinate systems: the cylindrical coordinates $\rho, z$ and the oblate spheroidal ones. A class of interior solutions matching with stationary axisymmetric asymptotically flat vacuum solutions is found in oblate spheroidal coordinates. The solutions presented satisfy the three energy conditions.Comment: Version published on IJMPD, title changed by the revie

Integrability of generalized (matrix) Ernst equations in string theory

The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\times 2d$-linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop ``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004, Gallipoli (Lecce), Italy. Minor typos, language and references corrections. To be published in the proceedings in Theor. Math. Phy