5,531 research outputs found
Polyhomogeneous expansions close to null and spatial infinity
A study of the linearised gravitational field (spin 2 zero-rest-mass field)
on a Minkowski background close to spatial infinity is done. To this purpose, a
certain representation of spatial infinity in which it is depicted as a
cylinder is used. A first analysis shows that the solutions generically develop
a particular type of logarithmic divergence at the sets where spatial infinity
touches null infinity. A regularity condition on the initial data can be
deduced from the analysis of some transport equations on the cylinder at
spatial infinity. It is given in terms of the linearised version of the Cotton
tensor and symmetrised higher order derivatives, and it ensures that the
solutions of the transport equations extend analytically to the sets where
spatial infinity touches null infinity. It is later shown that this regularity
condition together with the requirement of some particular degree of tangential
smoothness ensures logarithm-free expansions of the time development of the
linearised gravitational field close to spatial and null infinities.Comment: 24 pages, 5 figures. To appear in: The Conformal Structure of
Spacetimes. Geometry, Analysis, Numerics. J. Frauendiner and H. Friedrich
eds. Springe
A new class of obstructions to the smoothness of null infinity
Expansions of the gravitational field arising from the development of
asymptotically Euclidean, time symmetric, conformally flat initial data are
calculated in a neighbourhood of spatial and null infinities up to order 6. To
this ends a certain representation of spatial infinity as a cylinder is used.
This set up is based on the properties of conformal geodesics. It is found that
these expansions suggest that null infinity has to be non-smooth unless the
Newman-Penrose constants of the spacetime, and some other higher order
quantities of the spacetime vanish. As a consequence of these results it is
conjectured that similar conditions occur if one were to take the expansions to
even higher orders. Furthermore, the smoothness conditions obtained suggest
that if a time symmetric initial data which is conformally flat in a
neighbourhood of spatial infinity yields a smooth null infinity, then the
initial data must in fact be Schwarzschildean around spatial infinity.Comment: 24 pages, 4 figure
Characteristics and dynamics of surfzone transverse finger bars
Patches of transverse finger bars have been identified in the surf zone of Noordwijk
beach (Netherlands). They consisted of three to nine elongated accumulations of sand
attached to the low-tide shoreline. The bars extended up to 50 m into the inner surf zone,
had an oblique orientation with respect to the shore-normal, and were quasiregularly
spaced in the alongshore direction.Postprint (published version
Asymptotic properties of the development of conformally flat data near spatial infinity
Certain aspects of the behaviour of the gravitational field near null and
spatial infinity for the developments of asymptotically Euclidean, conformally
flat initial data sets are analysed. Ideas and results from two different
approaches are combined: on the one hand the null infinity formalism related to
the asymptotic characteristic initial value problem and on the other the
regular Cauchy initial value problem at spatial infinity which uses Friedrich's
representation of spatial infinity as a cylinder. The decay of the Weyl tensor
for the developments of the class of initial data under consideration is
analysed under some existence and regularity assumptions for the asymptotic
expansions obtained using the cylinder at spatial infinity. Conditions on the
initial data to obtain developments satisfying the Peeling Behaviour are
identified. Further, the decay of the asymptotic shear on null infinity is also
examined as one approaches spatial infinity. This decay is related to the
possibility of selecting the Poincar\'e group out of the BMS group in a
canonical fashion. It is found that for the class of initial data under
consideration, if the development peels, then the asymptotic shear goes to zero
at spatial infinity. Expansions of the Bondi mass are also examined. Finally,
the Newman-Penrose constants of the spacetime are written in terms of initial
data quantities and it is shown that the constants defined at future null
infinity are equal to those at past null infinity.Comment: 24 pages, 1 figur
The "non-Kerrness" of domains of outer communication of black holes and exteriors of stars
In this article we construct a geometric invariant for initial data sets for
the vacuum Einstein field equations , such that
is a 3-dimensional manifold with an asymptotically Euclidean end
and an inner boundary with the topology of the 2-sphere.
The hypersurface can be though of being in the domain of outer
communication of a black hole or in the exterior of a star. The geometric
invariant vanishes if and only if is an initial
data set for the Kerr spacetime. The construction makes use of the notion of
Killing spinors and of an expression for a \emph{Killing spinor candidate}
which can be constructed out of concomitants of the Weyl tensor.Comment: 13 page
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