General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2

On smoothness-asymmetric null infinities

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.Comment: 13 pages, 1 figur

The near-synchronous polar V1432 Aql (RX J1940.1-1025): Accretion geometry and synchronization time scale

The magnetic Cataclysmic Variable (mCV) V1432 Aql (RX 1940.1-1025) belongs to the four-member subclass of near-synchronous polars with a slight non-synchronism (<2 %) between the spin period of the white dwarf and the binary period. In these systems the accretion geometry changes periodically with phase of the beat cycle. We present the application of a dipole accretion model for near-synchronous systems developed by Geckeler & Staubert (1997a) to extended optical and X-ray data. We detect a significant secular change of the white dwarf spin period in V1432 Aql of dP_spin/dt = -5.4 (+3.7/-3.2) 10-9 s/s from the optical data set alone. This corresponds to a synchronization time scale tau_sync = 199 (+441/-75) yr, comparable to the time scale of 170 yr for V1500 Cyg. The synchronization time scale in V1432 Aql is in excellent agreement with the theoretical prediction from the dominating magnetic torque in near-synchronous systems. We also present period analyses of optical CCD photometry and RXTE X-ray data, which argue against the existence of a 4000 s period and an interpretation of V1432 Aql as an intermediate polar. The dipole accretion model also allows to constrain the relevant parameters of the accretion geometry in this system: the optical data allow an estimate of the dimensionless parameter (R_t0'/R_wd)1/2 sin(beta) = 3.6 (+2.7/-1.1), with a lower limit for the threading radius of R_t0' > 10 R_wd (68% confidence).Comment: 12 pages, 10 figures, 6 tables accepted by A&

On a choice of the Bondi radial coordinate and news function for the axisymmetric two-body problem

In the Bondi formulation of the axisymmetric vacuum Einstein equations, we argue that the ``surface area'' coordinate condition determining the ``radial'' coordinate can be considered as part of the initial data and should be chosen in a way that gives information about the physical problem whose solution is sought. For the two-body problem, we choose this coordinate by imposing a condition that allows it to be interpreted, near infinity, as the (inverse of the) Newtonian potential. In this way, two quantities that specify the problem -- the separation of the two particles and their mass ratio -- enter the equations from the very beginning. The asymptotic solution (near infinity) is obtained and a natural identification of the Bondi "news function" in terms of the source parameters is suggested, leading to an expression for the radiated energy that differs from the standard quadrupole formula but agrees with recent non-linear calculations. When the free function of time describing the separation of the two particles is chosen so as to make the new expression agree with the classical result, closed-form analytic expressions are obtained, the resulting metric approaching the Schwarzschild solution with time. As all physical quantities are defined with respect to the flat metric at infinity, the physical interpretation of this solution depends strongly on how these definitions are extended to the near-zone and, in particular, how the "time" function in the near-zone is related to Bondi's null coordinate.Comment: 13 pages, LaTeX, submitted to Classical and Quantum Gravity; v2 corrected a few typos and added some comments; v3 expanded discussion and added references -- Rejected by CQG; v4: 8 pages revtex4 2 column, extensively revised, submitted to Phys Rev D; v5: 21 pages revtex4 preprint; further discussion of physical interpretation; v6: 21 pages revtex4 preprint -- final version to appear in Phys. Rev. D (2006

On "many black hole" space-times

We analyze the horizon structure of families of space times obtained by evolving initial data sets containing apparent horizons with several connected components. We show that under certain smallness conditions the outermost apparent horizons will also have several connected components. We further show that, again under a smallness condition, the maximal globally hyperbolic development of the many black hole initial data constructed by Chrusciel and Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an event horizon, the intersection of which with the initial data hypersurface is not connected. This justifies the "many black hole" character of those space-times.Comment: several graphic file

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review