1,133 research outputs found
Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
We consider asymptotically-flat, static and stationary solutions of the
Einstein equations representing Einstein-Maxwell space-times in which the
Maxwell field is not constant along the Killing vector defining stationarity,
so that the symmetry of the space-time is not inherited by the electromagnetic
field. We find that static degenerate black hole solutions are not possible
and, subject to stronger assumptions, nor are static, non-degenerate or
stationary black holes. We describe the possibilities if the stronger
assumptions are relaxed.Comment: 19 pages, to appear in GER
Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri
The structure of polyhomogeneous space-times (i.e., space-times with metrics
which admit an expansion in terms of ) constructed by a
Bondi--Sachs type method is analysed. The occurrence of some log terms in an
asymptotic expansion of the metric is related to the non--vanishing of the Weyl
tensor at Scri. Various quantities of interest, including the Bondi mass loss
formula, the peeling--off of the Riemann tensor and the Newman--Penrose
constants of motion are re-examined in this context.Comment: LaTeX, 28pp, CMA-MR14-9
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
Einstein equations in the null quasi-spherical gauge III: numerical algorithms
We describe numerical techniques used in the construction of our 4th order
evolution for the full Einstein equations, and assess the accuracy of
representative solutions. The code is based on a null gauge with a
quasi-spherical radial coordinate, and simulates the interaction of a single
black hole with gravitational radiation. Techniques used include spherical
harmonic representations, convolution spline interpolation and filtering, and
an RK4 "method of lines" evolution. For sample initial data of "intermediate"
size (gravitational field with 19% of the black hole mass), the code is
accurate to 1 part in 10^5, until null time z=55 when the coordinate condition
breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed
Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"
The main goal of this work consists in showing that the analytic solutions
for a class of characteristic problems for the Einstein vacuum equations have
an existence region larger than the one provided by the Cauchy-Kowalevski
theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove
this result we first describe a geometric way of writing the vacuum Einstein
equations for the characteristic problems we are considering, in a gauge
characterized by the introduction of a double null cone foliation of the
spacetime. Then we prove that the existence region for the analytic solutions
can be extended to a larger region which depends only on the validity of the
apriori estimates for the Weyl equations, associated to the "Bel-Robinson
norms". In particular if the initial data are sufficiently small we show that
the analytic solution is global. Before showing how to extend the existence
region we describe the same result in the case of the Burger equation, which,
even if much simpler, nevertheless requires analogous logical steps required
for the general proof. Due to length of this work, in this paper we mainly
concentrate on the definition of the gauge we use and on writing in a
"geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski
theorem is adapted to the characteristic problem for the Einstein equations and
we describe how the existence region can be extended in the case of the Burger
equation. Finally we describe the structure of the extension proof in the case
of the Einstein equations. The technical parts of this last result is the
content of a second paper.Comment: 68 page
Quantization of Gauge Field Theories on the Front-Form without Gauge Constraints I : The Abelian Case
Recently, we have proposed a new front-form quantization which treated both
the and the coordinates as front-form 'times.' This
quantization was found to preserve parity explicitly. In this paper we extend
this construction to local Abelian gauge fields . We quantize this theory using
a method proposed originally by Faddeev and Jackiw . We emphasize here the
feature that quantizing along both and , gauge theories does not
require extra constraints (also known as 'gauge conditions') to determine the
solution uniquely.Comment: 18 pages, phyzz
Ghost points in inverse scattering constructions of stationary Einstein metrics
We prove a removable singularities theorem for stationary Einstein equations,
with useful implications for constructions of stationary solutions using
soliton methods
Zur Klassifizierung mehrparametriger Dämpfungsmodelle
Vier Dämpfungsmodelle wurden in Nolte und Müller zum Hagen (2005) hinsichtlich ihrer mathematischen Struktur beschriebenen: Das Maxwell-Modell, das Jeffreys-Modell, das Kelvin-Voigt-Modell sowie das Poynting-Thomson-Modell. Die Diskussion der Modelle erfolgte an den partiellen Differentialgleichungen in der Verschiebung. Weitere physikalische Untersuchungen fanden statt. Es hat sich, dass zwei der partiellen Differentialgleichungen (Dämpfungsmodell nach Maxwell und Poynting-Thomson) rein hyperbolisch sind und die zwei anderen partiellen Differentialgleichungen vom parabolischen-hyperbolischen Typ sind. Diese Erkenntnis wird in dieser Arbeit auf mehrparametrige Dämpfungsmodelle übertragen
Static self-gravitating many-body systems in Einstein gravity
We consider the problem of constructing static, elastic, many-body systems in
Einstein gravity. The solutions constructed are deformations of static
many-body configurations in Newtonian gravity. No symmetry assumptions are
made.Comment: 15 page
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