2,029 research outputs found
The Newtonian limit of spacetimes describing uniformly accelerated particles
We discuss the Newtonian limit of boost-rotation symmetric spacetimes by
means of the Ehler's frame theory. Conditions for the existence of such a limit
are given and, in particular, we show that asymptotic flatness is an essential
requirement for the existence of such a limit. Consequently, generalized
boost-rotation symmetric spacetimes describing particles moving in uniform
fields will not possess a Newtonian limit. In the cases where the
boost-rotation symmetric spacetime is asymptotically flat and its Newtonian
limit exists, then it is non-zero only for the instant of time symmetry and its
value is given by a Poisson integral. The relation of this result with the
(Newtonian) gravitational potential suggested by the weak field approximation
is discussed. We illustrate our analysis through some examples: the two
monopoles solution, the Curzon-Chazy particle solution, the generalized
Bonnor-Swaminarayan solution, and the C metric.Comment: 19 pages, 4 figures and 1 appendix Minor corrections, one figure
removed. Version to appear in Proc. Roy. So
On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
It is proved that a stationary solutions to the vacuum Einstein field
equations with non-vanishing angular momentum have no Cauchy slice that is
maximal, conformally flat, and non-boosted. The proof is based on results
coming from a certain type of asymptotic expansions near null and spatial
infinity --which also show that the developments of Bowen-York type of data
cannot have a development admitting a smooth null infinity--, and from the fact
that stationary solutions do admit a smooth null infinity
On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields
The convergence of polyhomogeneous expansions of zero-rest-mass fields in
asymptotically flat spacetimes is discussed. An existence proof for the
asymptotic characteristic initial value problem for a zero-rest-mass field with
polyhomogeneous initial data is given. It is shown how this non-regular problem
can be properly recast as a set of regular initial value problems for some
auxiliary fields. The standard techniques of symmetric hyperbolic systems can
be applied to these new auxiliary problems, thus yielding a positive answer to
the question of existence in the original problem.Comment: 10 pages, 1 eps figur
Frustrated collisions and unconventional pairing on a quantum superlattice
We solve the problem of scattering and binding of two spin-1/2 fermions on a
one-dimensional superlattice with a period of twice the lattice spacing
analytically. We find the exact bound states and the scattering states,
consisting of a generalized Bethe ansatz augmented with an extra scattering
product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the
extra wave can be a bound state in the continuum corresponding to a
single-particle interband transition. In all other cases, it corresponds to a
quasi-momentum changing, frustrated collision.Comment: 4 pages, 2 figure
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
Geometric Invariant Measuring the Deviation from Kerr Data
A geometrical invariant for regular asymptotically Euclidean data for the
vacuum Einstein field equations is constructed. This invariant vanishes if and
only if the data correspond to a slice of the Kerr black hole spacetime --thus,
it provides a measure of the non-Kerr-like behavior of generic data. In order
to proceed with the construction of the geometric invariant, we introduce the
notion of approximate Killing spinors.Comment: 4 pages, added lemma, changed reference
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
Asymptotic simplicity and static data
The present article considers time symmetric initial data sets for the vacuum
Einstein field equations which in a neighbourhood of infinity have the same
massless part as that of some static initial data set. It is shown that the
solutions to the regular finite initial value problem at spatial infinity for
this class of initial data sets extend smoothly through the critical sets where
null infinity touches spatial infinity if and only if the initial data sets
coincide with static data in a neighbourhood of infinity. This result
highlights the special role played by static data among the class of initial
data sets for the Einstein field equations whose development gives rise to a
spacetime with a smooth conformal compactification at null infinity.Comment: 25 page
A rigidity property of asymptotically simple spacetimes arising from conformally flat data
Given a time symmetric initial data set for the vacuum Einstein field
equations which is conformally flat near infinity, it is shown that the
solutions to the regular finite initial value problem at spatial infinity
extend smoothly through the critical sets where null infinity touches spatial
infinity if and only if the initial data coincides with Schwarzschild data near
infinity.Comment: 37 page
Approximate twistors and positive mass
In this paper the problem of comparing initial data to a reference solution
for the vacuum Einstein field equations is considered. This is not done in a
coordinate sense, but through quantification of the deviation from a specific
symmetry. In a recent paper [T. B\"ackdahl, J.A. Valiente Kroon, Phys. Rev.
Lett. 104, 231102 (2010)] this problem was studied with the Kerr solution as a
reference solution. This analysis was based on valence 2 Killing spinors. In
order to better understand this construction, in the present article we analyse
the analogous construction for valence 1 spinors solving the twistor equation.
This yields an invariant that measures how much the initial data deviates from
Minkowski data. Furthermore, we prove that this invariant vanishes if and only
of the mass vanishes. Hence, we get a proof of the positivity of mass.Comment: 18 pages, corrected typos, updated reference
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