The Toronto Blessing and the Kundalini Experience: a Comparative Perspective

Hedendaags word die korrekte benadering jeens ander godsdienste gepropageer as dié van verdraagsaamheid. Daarmee word gepoog om aan elke godsdiens bestaansreg te verleen. Verder word gepoog om elke godsdiens in eie reg te verstaan, dus sonder vooroordele. Die benadering het egter ’n ander moontlik onverwagte aspek na die voorgrond gebring, naamlik dat daar ook ooreenkomste tussen verskillende godsdienste bestaan. Wat die saak meer interessant maak is dat van hierdie ooreenkomste sake is wat vroeër as eksklusief behorende tot die Christendom beskou is. Een so ’n interessante ooreenkoms word aangetref wanneer die sogenaamde geestelike ervarings wat gepaard gaan met die ‘Toronto Blessing’ in die Charismatiese beweging vergelyk word met die gepaardgaande ervarings van die ‘Kundalini Awakening’ in Hinduïsme. Hierdie ooreenkoms bring onvermydelik ’n skaduwee oor die aanspraak van sommige van die Charismate dat die ervarings van die ‘Toronto Blessing’ verklaar kan word as uitsluitlik die werk van die Heilige Gees binne ’n Christelike konteks. In hierdie studie word dit ondersoek of hierdie ervaringe wat deel vorm van die Toronto Blessing, beskou kan word as eksklusief behorende tot die Christendom, of is dit ervarings wat aangebring word deur die toepassing van sekere menslike tegnieke. Die konklusie waartoe in hierdie artikel gekom word, is dat die ervaringe van die Toronto Blessing nie eenvoudig allesinsluitend toegeskryf kan word aan die werk van die Heilige Gees nie

Comparisons of binary black hole merger waveforms

This a particularly exciting time for gravitational wave physics. Ground-based gravitational wave detectors are now operating at a sensitivity such that gravitational radiation may soon be directly detected, and recently several groups have independently made significant breakthroughs that have finally enabled numerical relativists to solve the Einstein field equations for coalescing black-hole binaries, a key source of gravitational radiation. The numerical relativity community is now in the position to begin providing simulated merger waveforms for use by the data analysis community, and it is therefore very important that we provide ways to validate the results produced by various numerical approaches. Here, we present a simple comparison of the waveforms produced by two very different, but equally successful approaches--the generalized harmonic gauge and the moving puncture methods. We compare waveforms of equal-mass black hole mergers with minimal or vanishing spins. The results show exceptional agreement for the final burst of radiation, with some differences attributable to small spins on the black holes in one case.Comment: Revtex 4, 5 pages. Published versio

The Relationship Between X-ray Luminosity and Duty Cycle for Dwarf Novae and their Specific Frequency in the Inner Galaxy

We measure the duty cycles for an existing sample of well observed, nearby dwarf novae using data from AAVSO, and present a quantitative empirical relation between the duty cycle of dwarf novae outbursts and the X-ray luminosity of the system in quiescence. We have found that $\log DC=0.63(\pm0.21)\times(\log L_{X}({\rm erg\,s^{-1}})-31.3)-0.95(\pm0.1)$, where DC stands for duty cycle. We note that there is intrinsic scatter in this relation greater than what is expected from purely statistical errors. Using the dwarf nova X-ray luminosity functions from \citet{Pretorius12} and \citet{Byckling10}, we compare this relation to the number of dwarf novae in the Galactic Bulge Survey which were identified through optical outbursts during an 8-day long monitoring campaign. We find a specific frequency of X-ray bright ($L_{X}>10^{31}\,{\rm erg\,s^{-1}}$) Cataclysmic Variables undergoing Dwarf Novae outbursts in the direction of the Galactic Bulge of $6.6\pm4.7\times10^{-5}\,M_{\odot}^{-1}$. Such a specific frequency would give a Solar neighborhood space density of long period CVs of $\rho=5.6\pm3.9\times10^{-6}\,$pc$^{-3}$. We advocate the use of specific frequency in future work, given that projects like LSST will detect DNe well outside the distance range over which $\rho\approx{\textrm const}$.Comment: 9 pagers, 4 figures Accepted for publication in MNRA

The Interpretations For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes

It is found that there exists an empirical linear relation between the high frequency \nhigh and low frequency \nlow of quasi-periodic oscillations (QPOs) for black hole candidate (BHC), neutron star (NS) and white dwarf (WD) in the binary systems, which spans five orders of magnitude in frequency. For the NS Z (Atoll) sources, $\nu_{high}$ and $\nu_{low}$ are identified as the lower kHz QPO frequency and horizontal branch oscillations (HBOs) \nh (broad noise components); for the black hole candidates and low-luminosity neutron stars, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the ``dwarf nova oscillations'' (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes $\nu_{high}$ to the Alfv\'en wave oscillation frequency at a preferred radius and $\nu_{low}$ to the same mechanism at another radius. Then, we can obtain \nlow = 0.08 \nhigh and the relation between the upper kHz QPO frequency \nt and HBO to be \nh \simeq 56 ({\rm Hz}) (\nt/{\rm kHz})^{2}, which are in accordance with the observed empirical relations. Furthermore, some implications of model are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude in frequency. \\Comment: 11 pages, 1 figure, accepted by PAS

Testing outer boundary treatments for the Einstein equations

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections.Comment: Modified to agree with version accepted for publication in Class. Quantum Gra

Reducing orbital eccentricity in binary black hole simulations

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQ

Revisiting Event Horizon Finders

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision

Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.Comment: 16 pages, 14 figures; replaced with published versio

Eccentric black hole-neutron star mergers: effects of black hole spin and equation of state

There is a high level of interest in black hole-neutron star binaries, not only because their mergers may be detected by gravitational wave observatories in the coming years, but also because of the possibility that they could explain a class of short duration gamma-ray bursts. We study black hole-neutron star mergers that occur with high eccentricity as may arise from dynamical capture in dense stellar regions such as nuclear or globular clusters. We perform general relativistic simulations of binaries with a range of impact parameters, three different initial black hole spins (zero, aligned and anti-aligned with the orbital angular momentum), and neutron stars with three different equations of state. We find a rich diversity across these parameters in the resulting gravitational wave signals and matter dynamics, which should also be reflected in the consequent electromagnetic emission. Before tidal disruption, the gravitational wave emission is significantly larger than perturbative predictions suggest for periapsis distances close to effective innermost stable separations, exhibiting features reflecting the zoom-whirl dynamics of the orbit there. Guided by the simulations, we develop a simple model for the change in orbital parameters of the binary during close encounters. Depending upon the initial parameters of the system, we find that mass transfer during non-merging close encounters can range from essentially zero to a sizable fraction of the initial neutron star mass. The same holds for the amount of material outside the black hole post-merger, and in some cases roughly half of this material is estimated to be unbound. We also see that non-merging close encounters generically excite large oscillations in the neutron star that are qualitatively consistent with f-modes.Comment: 19 pages, 13 figures, revised according to referee comment