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

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

A habitat-use model to determine essential fish habitat for juvenile brown shrimp (Farfantepenaeus aztecus) in Galveston Bay, Texas

A density prediction model for juvenile brown shrimp (Farfantepenaeus aztecus) was developed by using three bottom types, five salinity zones, and four seasons to quantify patterns of habitat use in Galveston Bay, Texas. Sixteen years of quantitative density data were used. Bottom types were vegetated marsh edge, submerged aquatic vegetation, and shallow nonvegetated bottom. Multiple regression was used to develop density estimates, and the resultant formula was then coupled with a geographical information system (GIS) to provide a spatial mosaic (map) of predicted habitat use. Results indicated that juvenile brown shrimp (0.50. These results indicate that this model may have a broader geographic application and is a plausible approach in refining current EFH designations for all Gulf of Mexico estuaries with similar geomorphological and hydrological characteristics

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

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

Momentum flow in black-hole binaries: II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins

Research on extracting science from binary-black-hole (BBH) simulations has often adopted a "scattering matrix" perspective: given the binary's initial parameters, what are the final hole's parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons' effective and coordinate velocities. To investigate the gauge dependence of our results, we compare pseudospectral and moving-puncture evolutions of physically similar initial data; although spectral and puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum. [Abstract abbreviated; full abstract also mentions additional results.]Comment: Submitted to Phys. Rev.

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

Association between intrarenal arterial resistance and diastolic dysfunction in type 2 diabetes

<p>Abstract</p> <p>Background</p> <p>In comparison to the well established changes in compliance that occur at the large vessel level in diabetes, much less is known about the changes in compliance of the cardiovascular system at the end-organ level. The aim of this study was therefore to examine whether there was a correlation between resistance of the intrarenal arteries of the kidney and compliance of the left ventricle, as estimated by measurements of diastolic function, in subjects with type 2 diabetes.</p> <p>Methods</p> <p>We studied 167 unselected clinic patients with type 2 diabetes with a kidney duplex scan to estimate intrarenal vascular resistance, i.e. the resistance index (RI = peak systolic velocity-minimum diastolic velocity/peak systolic velocity) and a transthoracic echocardiogram (TTE) employing tissue doppler studies to document diastolic and systolic ventricular function.</p> <p>Results</p> <p>Renal RI was significantly higher in subjects with diastolic dysfunction (0.72 ± 0.05) when compared with those who had a normal TTE examination (0.66 ± 0.06, p < 0.01). Renal RI values were correlated with markers of diastolic dysfunction including the E/Vp ratio (r = 0.41, p < 0.001), left atrial area (r = 0.36, p < 0.001), the E/A ratio (r = 0.36, p < 0.001) and the E/E' ratio (r = 0.31, p < 0.001). These associations were independent of systolic function, hypertension, the presence and severity of chronic kidney disease, the use of renin-angiotensin inhibitors and other potentially confounding variables.</p> <p>Conclusion</p> <p>Increasing vascular resistance of the intrarenal arteries was associated with markers of diastolic dysfunction in subjects with type 2 diabetes. These findings are consistent with the hypothesis that vascular and cardiac stiffening in diabetes are manifestations of common pathophysiological mechanisms.</p

TADPOL: A 1.3 mm Survey of Dust Polarization in Star-forming Cores and Regions

We present {\lambda}1.3 mm CARMA observations of dust polarization toward 30 star-forming cores and 8 star-forming regions from the TADPOL survey. We show maps of all sources, and compare the ~2.5" resolution TADPOL maps with ~20" resolution polarization maps from single-dish submillimeter telescopes. Here we do not attempt to interpret the detailed B-field morphology of each object. Rather, we use average B-field orientations to derive conclusions in a statistical sense from the ensemble of sources, bearing in mind that these average orientations can be quite uncertain. We discuss three main findings: (1) A subset of the sources have consistent magnetic field (B-field) orientations between large (~20") and small (~2.5") scales. Those same sources also tend to have higher fractional polarizations than the sources with inconsistent large-to-small-scale fields. We interpret this to mean that in at least some cases B-fields play a role in regulating the infall of material all the way down to the ~1000 AU scales of protostellar envelopes. (2) Outflows appear to be randomly aligned with B-fields; although, in sources with low polarization fractions there is a hint that outflows are preferentially perpendicular to small-scale B-fields, which suggests that in these sources the fields have been wrapped up by envelope rotation. (3) Finally, even at ~2.5" resolution we see the so-called "polarization hole" effect, where the fractional polarization drops significantly near the total intensity peak. All data are publicly available in the electronic edition of this article.Comment: 53 pages, 37 figures -- main body (13 pp., 3 figures), source maps (32 pp., 34 figures), source descriptions (8 pp.). Accepted by the Astrophysical Journal Supplemen

Viral Hepatitis and Rapid Diagnostic Test Based Screening for HBsAg in HIV-infected Patients in Rural Tanzania.

\ud \ud Co-infection with hepatitis B virus (HBV) is highly prevalent in people living with HIV in Sub-Saharan Africa. Screening for HBV surface antigen (HBsAg) before initiation of combination antiretroviral therapy (cART) is recommended. However, it is not part of diagnostic routines in HIV programs in many resource-limited countries although patients could benefit from optimized antiretroviral therapy covering both infections. Screening could be facilitated by rapid diagnostic tests for HBsAg. Operating experience with these point of care devices in HIV-positive patients in Sub-Saharan Africa is largely lacking. We determined the prevalence of HBV and Hepatitis C virus (HCV) infection as well as the diagnostic accuracy of the rapid test device Determine HBsAg in an HIV cohort in rural Tanzania. Prospectively collected blood samples from adult, HIV-1 positive and antiretroviral treatment-naïve patients in the Kilombero and Ulanga antiretroviral cohort (KIULARCO) in rural Tanzania were analyzed at the point of care with Determine HBsAg, a reference HBsAg EIA and an anti-HCV EIA. Samples of 272 patients were included. Median age was 38 years (interquartile range [IQR] 32-47), 169/272 (63%) subjects were females and median CD4+ count was 250 cells/µL (IQR 97-439). HBsAg was detected in 25/272 (9.2%, 95% confidence interval [CI] 6.2-13.0%) subjects. Of these, 7/25 (28%) were positive for HBeAg. Sensitivity of Determine HBsAg was rated at 96% (95% CI 82.8-99.6%) and specificity at 100% (95% CI, 98.9-100%). Antibodies to HCV (anti-HCV) were found in 10/272 (3.7%, 95% CI 2.0-6.4%) of patients. This study reports a high prevalence of HBV in HIV-positive patients in a rural Tanzanian setting. The rapid diagnostic test Determine HBsAg is an accurate assay for screening for HBsAg in HIV-1 infected patients at the point of care and may further help to guide cART in Sub-Saharan Africa