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

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

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

Carboplatin binding to a model protein in non-NaCl conditions to eliminate partial conversion to cisplatin, and the use of different criteria to choose the resolution limit

Hen egg white lysozyme (HEWL) co-crystallisation conditions of carboplatin without sodium chloride (NaCl) have been utilised to eliminate partial conversion of carboplatin to cisplatin observed previously. Tetragonal HEWL crystals were successfully obtained in 65% MPD with 0.1M citric acid buffer at pH 4.0 including DMSO. The X-ray diffraction data resolution to be used for the model refinement was reviewed using several topical criteria together. The CC1/2 criterion implemented in XDS led to data being significant to 2.0{\AA}, compared to the data only being able to be processed to 3.0{\AA} using the Bruker software package (SAINT). Then using paired protein model refinements and DPI values based on the FreeR value, the resolution limit was fine tuned to be 2.3{\AA}. Interestingly this was compared with results from the EVAL software package which gave a resolution limit of 2.2{\AA} solely using crossing 2, but 2.8{\AA} based on the Rmerge values (60%). The structural results showed that carboplatin bound to only the N{\delta} binding site of His-15 one week after crystal growth, whereas five weeks after crystal growth, two molecules of carboplatin are bound to the His-15 residue. In summary several new results have emerged: - firstly non-NaCl conditions showed a carboplatin molecule bound to His-15 of HEWL; secondly binding of one molecule of carboplatin was seen after one week of crystal growth and two molecules were bound after five weeks of crystal growth; and thirdly the use of several criteria to determine the diffraction resolution limit led to the successful use of data to higher resolution.Comment: 14 pages; submitted to Acta Cryst D Biological Crystallography reference number tz504

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

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

The conformal Einstein field equations with massless Vlasov matter

We prove the stability of de Sitter space-time as a solution to the Einstein–Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely Friedrich’s conformal Einstein field equations. We exploit the conformal invariance of the massless Vlasov equation on the cotangent bundle and adapt Kato’s local existence theorem for symmetric hyperbolic systems to prove a long enough time of existence for solutions of the evolution system implied by the Vlasov equation and the conformal Einstein field equations

Studying Attractor Symmetries by Means of Cross Correlation Sums

We use the cross correlation sum introduced recently by H. Kantz to study symmetry properties of chaotic attractors. In particular, we apply it to a system of six coupled nonlinear oscillators which was shown by Kroon et al. to have attractors with several different symmetries, and compare our results with those obtained by ``detectives" in the sense of Golubitsky et al.Comment: LaTeX file, 16 pages and 16 postscript figures; tarred, gzipped and uuencoded; submitted to 'Nonlinearity

Photoionization in the time and frequency domain

Ultrafast processes in matter, such as the electron emission following light absorption, can now be studied using ultrashort light pulses of attosecond duration ($10^{-18}$s) in the extreme ultraviolet spectral range. The lack of spectral resolution due to the use of short light pulses may raise serious issues in the interpretation of the experimental results and the comparison with detailed theoretical calculations. Here, we determine photoionization time delays in neon atoms over a 40 eV energy range with an interferometric technique combining high temporal and spectral resolution. We spectrally disentangle direct ionization from ionization with shake up, where a second electron is left in an excited state, thus obtaining excellent agreement with theoretical calculations and thereby solving a puzzle raised by seven-year-old measurements. Our experimental approach does not have conceptual limits, allowing us to foresee, with the help of upcoming laser technology, ultra-high resolution time-frequency studies from the visible to the x-ray range.Comment: 5 pages, 4 figure