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.

Hipomotilidad gastrointestinal en conejos : 7 casos clínicos

Se describen siete casos clínicos de hipomotilidad gastrointestinal (HGI) en conejos mantenidos como mascotas. En todos los casos se intenta establecer la causa primaria que inició el proceso de HGI. Finalmente se discuten las ventajas e inconvenientes de cada una de las medidas terapéuticas aplicadas.

Landau-Khalatnikov-Fradkin Gauge Transformations for the Propagator and Vertex in QED and QED₂

Abstract The non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformations describe how Green functions in quantum field theory transform under a change in the photon field’s linear covariant gauge parameter (denoted ξ). The transformations are framed most simply in coordinate space where they are multiplicative. They imply that information on gauge-dependent contributions from higher order diagrams in the perturbative series is contained in lower order contributions, which is useful in multi-loop calculations. We study the LKF transformations for the propagator and the vertex in both scalar and spinor QED, in some particular dimensions. A novelty of our work is to derive momentum-space integral representations of these transformations; our expressions are also applicable to the longitudinal and transverse parts of the vertex. Applying these transformations to the tree-level Green functions, we show that the one-loop terms obtained from the LKF transformation agree with the gauge dependent parts obtained from perturbation theory. Our results will be presented in more comprehensive form elsewhere.</jats:p

Tuning the Lewis Acidity of Boranes in Frustrated Lewis Pair Chemistry: Implications for the Hydrogenation of Electron-Poor Alkenes

An analysis of the metal-free reduction of electron deficient olefins by frustrated Lewis pairs indicates that the rate-determining step might be either the heterolytic cleavage of H2 to form an -onium borohydride salt, or the subsequent transfer of the hydride moiety to the substrate following a Michael-type addition reaction. While the use of strong Lewis acids such as B(C6F5)3 facilitates the first of these processes, hydride transfer to the olefin should be contrarily favoured by the use of weak Lewis acids which, for this very same reason, might be unable to promote the prior H2 split. After systematic testing of several boranes of different Lewis acidity (assessed by using the Childs’ method) and steric demand, an optimal situation that employs tris(2,4,6-trifluorophenyl)borane was reached. Mixtures of this borane with 1,4-diazabicyclo[2.2.2]octane (DABCO) exhibited excellent catalytic activity for the hydrogenation of alkylidene malonates. In fact, this transformation could be achieved under milder conditions than those we reported previously. Moreover, the reaction scope could be expanded to other electron deficient olefins containing esters, sulfones or nitro functionalities as electron-withdrawing substituents

Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations

We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for the treatment in the ``close limit approximation'' of the collision of counterrotating black holes.Comment: 12 pages RevTe

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent a 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. © 1998 The American Physical Society

Collision of boosted black holes: Second order close limit calculations

We study the head-on collision of black holes starting from unsymmetrized, Brill-Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the “close limit approximation,” in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions. © 1999 The American Physical Society

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 wave forms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order corrections to provide “error bars” to the first-order results 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 wave form templates for gravitational wave detection. © 1996 The American Physical Society

Gravitational radiation from Schwarzschild black holes: The second-order perturbation formalism

The perturbation theory of black holes has been useful recently for providing estimates of gravitational radiation from the black-hole collisions. Second-order perturbation theory, relatively undeveloped until recently, has proved to be important both for providing refined estimates and for indicating the range of validity of perturbation theory. Here we review the second-order formalism for perturbations of Schwarzschild spacetimes. The emphasis is on practical methods for carrying out the second-order computations of the outgoing radiation. General issues are illustrated throughout with examples from close-limit results, perturbation calculations in which black holes start from the small separation. © 2000 Elsevier Science B.V