Authors: David A. Nichols, Aaron Zimmerman, Yanbei Chen, Geoffrey Lovelace, Keith D. Matthews, Robert Owen, Fan Zhang, Kip S. Thorne
Date: 15 Aug 2012
Abstract: 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)ˆl] or magnetic [(-1)ˆ(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.]
Authors: Fan Zhang, Aaron Zimmerman, David A. Nichols, Yanbei Chen, Geoffrey Lovelace, Keith D. Matthews, Robert Owen, Kip S. Thorne
Date: 15 Aug 2012
Abstract: 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.]
Authors: Drew Keppel
Date: 11 Aug 2012
Abstract: We derive explicit expressions for the multi-detector F-statistic metric applied to short-duration non-precessing inspiral signals. This is required for template bank production associated with coherent searches for short-duration non-precessing inspiral signals in gravitational-wave data from a network of detectors. We compare the metric's performance with explicit overlap calculations for all relevant dimensions of parameter space and find the metric accurately predicts the loss of detection statistic above overlaps of 95%. We also show the effect that neglecting the variations of the detector response functions has on the metric.
Authors: Vladimir Dergachev
Date: 9 Aug 2012
Abstract: Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical model. We show how to implement statistical estimates of physical quantities (such as upper limits) that are valid without assuming a particular family of statistical distributions, while still providing close to optimal values when the data is from an expected distribution (such as Gaussian or exponential). This new technique can compute statistically sound results in the presence of severe non-Gaussian noise, relaxes assumptions on distribution stationarity and is especially useful in automated analysis of large datasets, where computational speed is important.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis