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

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

Zero rest-mass fields and the Newman-Penrose constants on flat space

Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman–Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich’s framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance ρ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic at a fixed order in ρ. In addition, it is shown that for generic initial data within the class considered in this article, there is no natural correspondence between the NP constants at future and past null infinity—for both the Maxwell and spin-2 field. However, if the initial data are time-symmetric, then the NP constants at future and past null infinity have the same information

Measurement of mRNA by quantitative PCR with a nonradioactive label

This report describes the development of a method to measure mRNA in small samples of human tissue by the polymerase chain reaction with a nonradioactive label. In this method RNA is reverse-transcribed in the presence of a control RNA, and subsequently amplified by the polymerase chain reaction during which a nonradioactive label (digoxigenin-11-dUTP) is incorporated. Gel blotting and immunological detection of digoxigenin followed by a chemiluminescent reaction provide an intense signal on film. This allows the detection and quantitation of 3-hydroxy-3-methylglutaryl (HMG) CoA reductase mRNA in 12 ng of RNA. We demonstrate that this is a sensitive and reproducible method, and that quantitation is linear with respect to the amount of mRNA present. The application of this method to the measurement of low density lipoprotein receptor and 3-hydroxy-3-methylglutaryl coenzyme A reductase mRNA levels in circulating peripheral blood mononuclear cells and human liver biopsy samples is discussed. The use of chemiluminescent reagents instead of radioactive labels allows this procedure to be performed safely in laboratories not equipped for radioactivity

Context dependent differences in working memory related brain activity in heavy cannabis users

Rationale  Compromised cognitive control in cannabis use–tempting situations is thought to play a key role in the development of cannabis use disorders. However, little is known about how exposure to cannabis cues and contexts may influence cognitive control and the underlying neural mechanisms in cannabis users.  Objectives  Working memory (WM) is an attention reliant executive function central to cognitive control. In this study, we investigated how distracting cannabis words affected WM load–dependent performance and related brain activity in near-daily cannabis users (N = 36) relative to controls (N = 33).  Methods  Brain activity was recorded during a novel N-back flanker WM task with neutral and cannabis flankers added as task-irrelevant distractors.  Results  On a behavioural level, WM performance did not differ between groups, and the presence of cannabis flankers did not affect performance. However, in cannabis users compared to controls, the presence of cannabis flankers reduced WM load–related activity in multiple regions, including the insula, thalamus, superior parietal lobe and supramarginal gyrus.  Conclusions  The group specificity of these effects suggest that cannabis users might differ from controls in the way they process cannabis-related cues and that cannabis cue exposure could interfere with other cognitive processes under cognitively demanding circumstances. Future studies should focus on the role of context in cognitive control–related processes like WM and attention to further elucidate potential cognitive impairments in heavy cannabis users and how these relate to loss of control over drug seeking itself