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

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 $(\mathcal{S},h_{ab},K_{ab})$, such that $\mathcal{S}$ is a 3-dimensional manifold with an asymptotically Euclidean end and an inner boundary $\partial \mathcal{S}$ with the topology of the 2-sphere. The hypersurface $\mathcal{S}$ 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 $(\mathcal{S},h_{ab},K_{ab})$ 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

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

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

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

Combinatorial optimization model for railway engine assignment problem

This paper presents an experimental study for the Hungarian State Railway Company (M\'AV). The engine assignment problem was solved at M\'AV by their experts without using any explicit operations research tool. Furthermore, the operations research model was not known at the company. The goal of our project was to introduce and solve an operations research model for the engine assignment problem on real data sets. For the engine assignment problem we are using a combinatorial optimization model. At this stage of research the single type train that is pulled by a single type engine is modeled and solved for real data. There are two regions in Hungary where the methodology described in this paper can be used and M\'AV started to use it regularly. There is a need to generalize the model for multiple type trains and multiple type engines