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

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

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 $r^{-2}\ln r$ is proposed. By contrast, in the smooth version the effects are of order $r^{-3}$. 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

Shunting of Passenger Train Units in a Railway Station

In this paper we introduce the problem of shunting passenger trainunits in a railway station. Shunting occurs whenever train units aretemporarily not necessary to operate a given timetable. We discussseveral aspects of this problem and focus on two subproblems. Wepropose mathematical models for these subproblems together with asolution method based on column generation. Furthermore, a newefficient and speedy solution technique for pricing problems in columngeneration algorithms is introduced. Finally, we present computationalresults based on real life instances from Netherlands Railways.logistics;column generation;railway optimization;real world application

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