Visualizing Spacetime Curvature via Gradient Flows II: An Example of the Construction of a Newtonian analogue

This is the first in a series of papers in which the gradient flows of fundamental curvature invariants are used to formulate a visualization of curvature. We start with the construction of strict Newtonian analogues (not limits) of solutions to Einstein's equations based on the topology of the associated gradient flows. We do not start with any easy case. Rather, we start with the Curzon - Chazy solution, which, as history shows, is one of the most difficult exact solutions to Einstein's equations to interpret physically. We show that the entire field of the Curzon - Chazy solution, up to a region very "close" to the the intrinsic singularity, strictly represents that of a Newtonian ring, as has long been suspected. In this regard, we consider our approach very successful. As regrades the local structure of the singularity of the Curzon - Chazy solution within a fully general relativistic analysis, however, whereas we make some advances, the full structure of this singularity remains incompletely resolved.Comment: 12 pages twocolumn revtex 4-1 9 figures. Expanded and correcte

The McVittie solution with a negative cosmological constant

Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant ($\Lambda > 0$), the AdS/CFT correspondence tells us that the case $\Lambda<0$ is still worthy of consideration. In this paper we study the McVittie solution with $\Lambda<0$. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson - Walker case, we find that $\Lambda<0$ ensures collapse to a Big Crunch, a feature which completely dominates the global structure.Comment: 6 pages twocolumn revtex 4-1 8 figures updated references Final form to appear in Phys Rev

Decaying Dark Matter and the Deficit of Dwarf Haloes

The hierarchical clustering inherent in Lambda-CDM cosmology seems to produce many of the observed characteristics of large-scale structure. But some glaring problems still remain, including the over-prediction (by a factor 10) of the number of dwarf galaxies within the virialized population of the local group. Several secondary effects have already been proposed to resolve this problem. It is still not clear, however, whether the principal solution rests with astrophysical processes, such as early feedback from supernovae, or possibly with as yet undetermined properties of the dark matter itself. In this paper, we carry out a detailed calculation of the dwarf halo evolution incorporating the effects of a hypothesized dark-matter decay, D -> D'+l, where D is the unstable particle, D' is the more massive daughter particle and l is the other, lighter (or possibly massless) daughter particle. This process preferentially heats the smaller haloes, expanding them during their evolution and reducing their present-day circular velocity. We find that this mechanism can account very well for the factor 4 deficit in the observed number of systems with velocity 10--20 km/s compared to those predicted by the numerical simulations, if dm/m_D' ~ 5-7 x 10^{-5}, where dm is the mass difference between the initial and final states. The corresponding lifetime tau cannot be longer than ~30 Gyr, but may be as short as just a few Gyr.Comment: 19 pages, 6 figures, Accepted for publication in MNRA

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

SummaryBackground Azithromycin has been proposed as a treatment for COVID-19 on the basis of its immunomodulatoryactions. We aimed to evaluate the safety and efficacy of azithromycin in patients admitted to hospital with COVID-19.Methods In this randomised, controlled, open-label, adaptive platform trial (Randomised Evaluation of COVID-19Therapy [RECOVERY]), several possible treatments were compared with usual care in patients admitted to hospitalwith COVID-19 in the UK. The trial is underway at 176 hospitals in the UK. Eligible and consenting patients wererandomly allocated to either usual standard of care alone or usual standard of care plus azithromycin 500 mg once perday by mouth or intravenously for 10 days or until discharge (or allocation to one of the other RECOVERY treatmentgroups). Patients were assigned via web-based simple (unstratified) randomisation with allocation concealment andwere twice as likely to be randomly assigned to usual care than to any of the active treatment groups. Participants andlocal study staff were not masked to the allocated treatment, but all others involved in the trial were masked to theoutcome data during the trial. The primary outcome was 28-day all-cause mortality, assessed in the intention-to-treatpopulation. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936.Findings Between April 7 and Nov 27, 2020, of 16 442 patients enrolled in the RECOVERY trial, 9433 (57%) wereeligible and 7763 were included in the assessment of azithromycin. The mean age of these study participants was65·3 years (SD 15·7) and approximately a third were women (2944 [38%] of 7763). 2582 patients were randomlyallocated to receive azithromycin and 5181 patients were randomly allocated to usual care alone. Overall,561 (22%) patients allocated to azithromycin and 1162 (22%) patients allocated to usual care died within 28 days(rate ratio 0·97, 95% CI 0·87–1·07; p=0·50). No significant difference was seen in duration of hospital stay (median10 days [IQR 5 to >28] vs 11 days [5 to >28]) or the proportion of patients discharged from hospital alive within 28 days(rate ratio 1·04, 95% CI 0·98–1·10; p=0·19). Among those not on invasive mechanical ventilation at baseline, nosignificant difference was seen in the proportion meeting the composite endpoint of invasive mechanical ventilationor death (risk ratio 0·95, 95% CI 0·87–1·03; p=0·24).Interpretation In patients admitted to hospital with COVID-19, azithromycin did not improve survival or otherprespecified clinical outcomes. Azithromycin use in patients admitted to hospital with COVID-19 should be restrictedto patients in whom there is a clear antimicrobial indication