8,389 research outputs found
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 () 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 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
- …