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

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

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

Applying Operations Research techniques to planning of train shunting

In this paper, we discuss a model-based algorithmic approach for supporting planners in the creation of shunt plans for passenger trains. The approach provides an example of a mathematical model and a corresponding solution approach for model based support. We introduce a four-step solution approach and we discuss how the planners are supported by this approach. Finally, we present computational results for these steps and give some suggestions for further research.A* search;railway optimization;real world application;routing

Polyhomogeneity and zero-rest-mass fields with applications to Newman-Penrose constants

A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and $\ln r$) for zero-rest-mass fields and gravity and its relation with the Newman-Penrose (NP) constants is given. It is shown that for spin-$s$ zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms in the asymptotic expansion appear naturally if the field does not obey the ``Peeling theorem''. The terms that give rise to the slower fall-off admit a natural interpretation in terms of advanced field. The connection between such fields and the NP constants is also discussed. The case when the background spacetime is curved and polyhomogeneous (in general) is considered. The free fields have to be polyhomogeneous, but the logarithmic terms due to the connection appear at higher powers of $1/r$. In the case of gravity, it is shown that it is possible to define a new auxiliary field, regular at null infinity, and containing some relevant information on the asymptotic behaviour of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future infinity ($i^+$)'' yields the logarithmic NP constants.Comment: 19 page

Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data

The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which are asymptotically Euclidean, conformally flat and time asymmetric. Our analysis allows for initial data whose second fundamental form is more general than the one given by the standard Bowen-York Ansatz. The Conformal Einstein equations imply upon evaluation on the cylinder at spatial infinity a hierarchy of transport equations which can be used to calculate in a recursive way asymptotic expansions for the gravitational field. It is found that the the solutions to these transport equations develop logarithmic divergences at certain critical sets where null infinity meets spatial infinity. Associated to these, there is a series of quantities expressible in terms of the initial data (obstructions), which if zero, preclude the appearance of some of the logarithmic divergences. The obstructions are, in general, time asymmetric. That is, the obstructions at the intersection of future null infinity with spatial infinity are different, and do not generically imply those obtained at the intersection of past null infinity with spatial infinity. The latter allows for the possibility of having spacetimes where future and past null infinity have different degrees of smoothness. Finally, it is shown that if both sets of obstructions vanish up to a certain order, then the initial data has to be asymptotically Schwarzschildean to some degree.Comment: 32 pages. First part of a series of 2 papers. Typos correcte

Explaining employees’ reactions towards a cross-border merger:the role of English language fluency

In this paper, we focus on the role of language in cross-border mergers and acquisitions and explore how organization members’ language skills, or fluency, in the adopted lingua franca may impact their reactions to a merger. Drawing on a qualitative study of the post-merger integration between a French and Dutch airline where English was adopted as a lingua franca, we illustrate how language fluency influences the ability of individuals to give meaning to their changed circumstances. Moreover, we elaborate on how language fluency indexes social groupings and identities, and may thus be a driver of perceptions of status inequality and identity politics between different groups of employees. With our study we draw attention to the multi-faceted role of English as a lingua franca. Our findings also contribute to research on sociocultural dynamics associated with post-merger integration and the role of language in mergers and acquisitions, as well as in multinational companies more generally

The conformal Einstein field equations and the local extension of future null infinity

We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces ⋆ and ′⋆ such that the conformal factor (but not its gradient) vanishes on a section of ⋆, one recovers a portion of null infinity. This result combined with the theory of the hyperboloidal initial value problem for the conformal Einstein field equations allows us to show the semi-global stability of the Minkowski spacetime from characteristic initial data