Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field $E$, which produces tidal forces, and the frame-drag field $B$, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of $E$) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of $E$ and $B$ on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities ($E$, $B$, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. [Abstract is abbreviated.]Comment: 19 pages, 7 figures, v2: Changed to reflect published version (changes made to color scales in Figs 5, 6, and 7 for consistent conventions). v3: Fixed Ref

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes III. Quasinormal Pulsations of Schwarzschild and Kerr Black Holes

In recent papers, we and colleagues have introduced a way to visualize the full vacuum Riemann curvature tensor using frame-drag vortex lines and their vorticities, and tidal tendex lines and their tendicities. We have also introduced the concepts of horizon vortexes and tendexes and 3-D vortexes and tendexes (regions where vorticities or tendicities are large). Using these concepts, we discover a number of previously unknown features of quasinormal modes of Schwarzschild and Kerr black holes. These modes can be classified by mode indexes (n,l,m), and parity, which can be electric [(-1)^l] or magnetic [(-1)^(l+1)]. Among our discoveries are these: (i) There is a near duality between modes of the same (n,l,m): a duality in which the tendex and vortex structures of electric-parity modes are interchanged with the vortex and tendex structures (respectively) of magnetic-parity modes. (ii) This near duality is perfect for the modes' complex eigenfrequencies (which are well known to be identical) and perfect on the horizon; it is slightly broken in the equatorial plane of a non-spinning hole, and the breaking becomes greater out of the equatorial plane, and greater as the hole is spun up; but even out of the plane for fast-spinning holes, the duality is surprisingly good. (iii) Electric-parity modes can be regarded as generated by 3-D tendexes that stick radially out of the horizon. As these "longitudinal," near-zone tendexes rotate or oscillate, they generate longitudinal-transverse near-zone vortexes and tendexes, and outgoing and ingoing gravitational waves. The ingoing waves act back on the longitudinal tendexes, driving them to slide off the horizon, which results in decay of the mode's strength. (iv) By duality, magnetic-parity modes are driven in this same manner by longitudinal, near-zone vortexes that stick out of the horizon. [Abstract abridged.]Comment: 53 pages with an overview of major results in the first 11 pages, 26 figures. v2: Very minor changes to reflect published version. v3: Fixed Ref

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications

When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free (STF) tensors: (i) the Weyl tensor's so-called "electric" part or tidal field, and (ii) the Weyl tensor's so-called "magnetic" part or frame-drag field. Being STF, the tidal field and frame-drag field each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of the tidal field's eigenvectors tendex lines, we call each tendex line's eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for the frame-drag field are vortex lines, their vorticities, and vortexes. We build up physical intuition into these concepts by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side by side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. [Abstract is abbreviated; full abstract also mentions additional results.]Comment: 25 pages, 20 figures, matches the published versio

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure

Detection of prions in the faeces of sheep naturally infected with classical scrapie

Classical scrapie is a naturally transmitted prion disease of sheep and goats. Contaminated environments may contribute to the spread of disease and evidence from animal models has implicated urine, blood, saliva, placenta and faeces as possible sources of the infection. Here we sought to determine whether sheep naturally infected with classical scrapie shed prions in their faeces. We used serial protein misfolding cyclic amplification (sPMCA) along with two extraction methods to examine faeces from sheep during both the clinical and preclinical phases of the disease and showed amplification of PrPSc in 7 of 15 and 14 of 14 sheep respectively. However PrPSc was not amplified from the faeces of 25 sheep not exposed to scrapie. These data represent the first demonstration of prion shedding in faeces from a naturally infected host and thus a likely source of prion contamination in the environment

A Six-Gene Signature Predicts Survival of Patients with Localized Pancreatic Ductal Adenocarcinoma

Jen Jen Yeh and colleagues developed and validated a six-gene signature in patients with pancreatic ductal adenocarcinoma that may be used to better stage the disease in these patients and assist in treatment decisions

The nationwide impact of COVID-19 on life support courses. A retrospective evaluation by Resuscitation Council UK

Aim: To determine the impact of the COVID-19 pandemic on Resuscitation Council UK Advanced Life Support (ALS) and Immediate Life Support (ILS) course numbers and outcomes. Methods: We conducted a before-after study using course data from the Resuscitation Council UK Learning Management System between January 2018 and December 2021, using 23 March 2020 as the cut-off between pre- and post-pandemic periods. Demographics and outcomes were analysed using chi-squared tests and regression models. Results: There were 90,265 ALS participants (51,464 pre-; 38,801 post-) and 368,140 ILS participants (225,628 pre-; 142,512 post-). There was a sharp decline in participants on ALS/ILS courses due to COVID-19. ALS participant numbers rebounded to exceed pre-pandemic levels, whereas ILS numbers recovered to a lesser degree with increased uptake of e-learning versions. Mean ALS course participants reduced from 20.0 to 14.8 post-pandemic (P < 0.001). Post-pandemic there were small but statistically significant decreases in ALS Cardiac Arrest Simulation Test pass rates (from 82.1 % to 80.1 % (OR = 0.90, 95 % CI = 0.86–0.94, P < 0.001)), ALS MCQ score (from 86.6 % to 86.0 % (mean difference = -0.35, 95 % CI −0.44 to −0.26, P < 0.001)), and overall ALS course results (from 95.2 %to 94.7 %, OR = 0.92, CI = 0.85–0.99, P = 0.023). ILS course outcomes were similar post-pandemic (from 99.4 % to 99.4 %, P = 0.037). Conclusion: COVID-19 caused a sharp decline in the number of participants on ALS/ILS courses and an accelerated uptake of e-learning versions, with the average ALS course size reducing significantly. The small reduction in performance on ALS courses requires further research to clarify the contributing factors

Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.Comment: 56 pages, 25 figures; various clarifications; accepted to CQ

Future perspectives in melanoma research. Meeting report from the "Melanoma Research: a bridge Naples-USA. Naples, December 6th-7 th2010"

Progress in understanding the molecular basis of melanoma has made possible the identification of molecular targets with important implications in clinical practice. In fact, new therapeutic approaches are emerging from basic science and it will be important to implement their rapid translation into clinical practice by active clinical investigation