Coordination Compounds of Alkali Metal Halides and Racemic Diaryl Diamines

Solid alkali metal coordination compounds of water soluble alkali metal salts of monobasic acids and racemic diamines are made by contacting an aqueous solution of the alkali metal salts with a solution of a racemic diamine compound of the formula wherein Ar in an aryl ring, X is alkyl and Y is alkyl or hydrogen, the X\u27s being different from the Y\u27s. The formation of the new coordination compounds provides a method for separation of alkali metal from alkaline earth metals

Nonexistence of conformally flat slices of the Kerr spacetime

Initial data for black hole collisions are commonly generated using the Bowen-York approach based on conformally flat 3-geometries. The standard (constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not conformally flat, so that use of the Bowen-York approach is limited in dealing with rotating holes. We investigate here whether there exist foliations of the Kerr spacetime that are conformally flat. We limit our considerations to foliations that are axisymmetric and that smoothly reduce in the Schwarzschild limit to slices of constant Schwarzschild time. With these restrictions, we show that no conformally flat slices can exist.Comment: 5 LaTeX pages; no figures; to be submitted to Phys. Rev.

Generalized LKF transformations for NN-point fermion correlators in QED

Within the worldline approach to quantum electrodynamics (QED), a change of the photon's covariant gauge parameter $\xi$ is investigated to analyse the non-perturbative gauge dependence of the configuration space fermion correlation functions, deriving a generalization of the Landau-Kalatnikov-Fradkin transformations (LKFt). These transformations reveal how the non-perturbative gauge dependence of position space amplitudes can be absorbed into a multiplicative exponential factor.Comment: Prepared for the Proceedings of the 20th Lomonosov Conference on Elementary Particle Physics, held in August 2021, based on a talk given by Jos\'e Nicasio on the results of arXiv:2012.10536 [hep-th] and arXiv:2010.04160 [hep-th

Colliding black holes: how far can the close approximation go?

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.Comment: 6 pages, RevTeX, 2 figures included with eps

The Efficiency of Gravitational Bremsstrahlung Production in the Collision of Two Schwarzschild Black Holes

We examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We constructed initial data for the characteristic initial value problem in Robinson-Trautman spacetimes, that represent two instantaneously stationary Schwarzschild black holes in motion towards each other with the same velocity. The Robinson-Trautman equation was integrated for these initial data using a numerical code based on the Galerkin method. The final resulting configuration is a boosted black hole with Bondi mass greater than the sum of the individual mass of each initial black hole. Two relevant aspects of the process are presented. The first relates the efficiency $\Delta$ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a distribution function of non-extensive thermostatistics with entropic parameter $q \simeq 1/2$; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second is a typical bremsstrahlung angular pattern in the early period of emission at the wave zone, a consequence of the deceleration of the black holes as they coalesce; this pattern evolves to a quadrupole form for later times.Comment: 16 pages, 4 figures, to appear in Int. J. Modern Phys. D (2008

Making use of geometrical invariants in black hole collisions

We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context of black hole perturbations $\cal S$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes ${\cal S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.Comment: 4 pages, 3 eps figures, Revte

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi