215 research outputs found
Asymptotic properties of the C-Metric
The aim of this article is to analyze the asymptotic properties of the
C-metric, using a general method specified in work of Tafel and coworkers, [1],
[2], [3]. By finding an appropriate conformal factor , it allows the
investigation of the asymptotic properties of a given asymptotically flat
spacetime. The news function and Bondi mass aspect are computed, their general
properties are analyzed, as well as the small mass, small acceleration, small
and large Bondi time limits.Comment: 28 pages, 11 figure
Nonclassical Symmetry Reduction and Riemann Wave Solutions
AbstractIn this paper we employ the “nonclassical symmetry method” in order to obtain Riemann multiple wave solutions of a system of first-order quasilinear differential equations. We show how to construct a Lie module of vector fields which are symmetries of the system supplemented by certain first-order differential constraints. We demonstrate the usefulness of our approach on several examples
Lagrangian and Hamiltonian for the Bondi-Sachs metrics
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the
Einstein vacuum equations in a closed form. Following the Dirac approach to
constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page
On the well posedness of Robinson Trautman Maxwell solutions
We show that the so called Robinson-Trautman-Maxwell equations do not
constitute a well posed initial value problem. That is, the dependence of the
solution on the initial data is not continuous in any norm built out from the
initial data and a finite number of its derivatives. Thus, they can not be used
to solve for solutions outside the analytic domain.Comment: 9 page
A model problem for the initial-boundary value formulation of Einstein's field equations
In many numerical implementations of the Cauchy formulation of Einstein's
field equations one encounters artificial boundaries which raises the issue of
specifying boundary conditions. Such conditions have to be chosen carefully. In
particular, they should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically desirable
properties like, for instance, minimizing reflections of gravitational
radiation.
Motivated by the problem in General Relativity, we analyze a model problem,
consisting of a formulation of Maxwell's equations on a spatially compact
region of spacetime with timelike boundaries. The form in which the equations
are written is such that their structure is very similar to the
Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field
equations. For this model problem, we specify a family of Sommerfeld-type
constraint-preserving boundary conditions and show that the resulting
initial-boundary value formulations are well posed. We expect that these
results can be generalized to the Einstein-Christoffel formulations of General
Relativity, at least in the case of linearizations about a stationary
background.Comment: 25 page
Anti-self-dual conformal structures with null Killing vectors from projective structures
Using twistor methods, we explicitly construct all local forms of
four--dimensional real analytic neutral signature anti--self--dual conformal
structures with a null conformal Killing vector. We show that is
foliated by anti-self-dual null surfaces, and the two-dimensional leaf space
inherits a natural projective structure. The twistor space of this projective
structure is the quotient of the twistor space of by the group action
induced by the conformal Killing vector.
We obtain a local classification which branches according to whether or not
the conformal Killing vector is hyper-surface orthogonal in . We give
examples of conformal classes which contain Ricci--flat metrics on compact
complex surfaces and discuss other conformal classes with no Ricci--flat
metrics.Comment: 43 pages, 4 figures. Theorem 2 has been improved: ASD metrics are
given in terms of general projective structures without needing to choose
special representatives of the projective connection. More examples (primary
Kodaira surface, neutral Fefferman structure) have been included. Algebraic
type of the Weyl tensor has been clarified. Final version, to appear in
Commun Math Phy
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