On the falloff of radiated energy in black hole spacetimes

The goal of much research in relativity is to understand gravitational waves generated by a strong-field dynamical spacetime. Quantities of particular interest for many calculations are the Weyl scalar $\psi_4$, which is simply related to the flux of gravitational waves far from the source, and the flux of energy carried to distant observers, $\dot E$. Conservation laws guarantee that, in asympotically flat spacetimes, $\psi_4 \propto 1/r$ and $\dot E \propto 1/r^2$ as $r \to \infty$. Most calculations extract these quantities at some finite extraction radius. An understanding of finite radius corrections to $\psi_4$ and $\dot E$ allows us to more accurately infer their asymptotic values from a computation. In this paper, we show that, if the final state of the system is a black hole, then the leading correction to $\psi_4$ is ${\cal O}(1/r^3)$, and that to the energy flux is ${\cal O}(1/r^4)$ --- not ${\cal O}(1/r^2)$ and ${\cal O}(1/r^3)$ as one might naively guess. Our argument only relies on the behavior of the curvature scalars for black hole spacetimes. Using black hole perturbation theory, we calculate the corrections to the leading falloff, showing that it is quite easy to correct for finite extraction radius effects.Comment: 5 pages, no figures, accepted to Phys. Rev. D. This version corrects several typos and minor errors in the earlier submissio

A Fuzzy Logic Based Algorithm for Finding Astronomical Objects in Wide-Angle Frames

Accurate automatic identification of astronomical objects in an imperfect world of non-linear wide-angle optics, imperfect optics, inaccurately pointed telescopes, and defect-ridden cameras is not always a trivial first step. In the past few years, this problem has been exacerbated by the rise of digital imaging, providing vast digital streams of astronomical images and data. In the modern age of increasing bandwidth, human identifications are many times impracticably slow. In order to perform an automatic computer-based analysis of astronomical frames, a quick and accurate identification of astronomical objects is required. Such identification must follow a rigorous transformation from topocentric celestial coordinates into image coordinates on a CCD frame. This paper presents a fuzzy logic based algorithm that estimates needed coordinate transformations in a practical setting. Using a training set of reference stars, the algorithm statically builds a fuzzy logic model. At runtime, the algorithm uses this model to associate stellar objects visible in the frames to known-catalogued objects, and generates files that contain photometry information of objects visible in the frame. Use of this algorithm facilitates real-time monitoring of stars and bright transients, allowing identifications and alerts to be issued more reliably. The algorithm is being implemented by the Night Sky Live all-sky monitoring global network and has shown itself significantly more reliable than the previously used non-fuzzy logic algorithm.Comment: Accepted for publication in PAS

Uniaxial magnetocrystalline anisotropy in CaRuO3{\rm CaRuO_3}

${\rm CaRuO_3}$ is a paramagnetic metal and since its low temperature resistivity is described by $\rho=\rho_0+AT^\gamma$ with $\gamma \sim 1.5$, it is also considered a non-Fermi liquid (NFL) metal. We have performed extensive magnetoresistance and Hall effect measurements of untwinned epitaxial films of ${\rm CaRuO_3}$. These measurements reveal that ${\rm CaRuO_3}$ exhibits uniaxial magnetocrystalline anisotropy. In addition, the low-temperature NFL behavior is most effectively suppressed when a magnetic field is applied along the easy axis, suggesting that critical spin fluctuations, possibly due to proximity of a quantum critical phase transition, are related to the NFL behavior.Comment: 7 figure

Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits

Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be computed using time--domain methods with accuracy that is fast approaching that of frequency--domain methods. We study in detail the computational efficiency of these methods for equatorial orbits of fast spinning Kerr black holes, and find the number of modes needed in either method --as functions of the orbital parameters-- in order to achieve a desired accuracy level. We then estimate the total computation time and argue that for high eccentricity orbits the time--domain approach is more efficient computationally. We suggest that in practice low--$m$ modes are computed using the frequency--domain approach, and high--$m$ modes are computed using the time--domain approach, where $m$ is the azimuthal mode number.Comment: 19 figures, 6 table

Late-time Kerr tails: generic and non-generic initial data sets, "up" modes, and superposition

Three interrelated questions concerning Kerr spacetime late-time scalar-field tails are considered numerically, specifically the evolutions of generic and non-generic initial data sets, the excitation of "up" modes, and the resolution of an apparent paradox related to the superposition principle. We propose to generalize the Barack-Ori formula for the decay rate of any tail multipole given a generic initial data set, to the contribution of any initial multipole mode. Our proposal leads to a much simpler expression for the late-time power law index. Specifically, we propose that the late-time decay rate of the $Y_{\ell m}$ spherical harmonic multipole moment because of an initial $Y_{\ell' m}$ multipole is independent of the azimuthal number $m$, and is given by $t^{-n}$, where $n=\ell'+\ell+1$ for $\ell<\ell'$ and $n=\ell'+\ell+3$ for $\ell\ge\ell'$. We also show explicitly that the angular symmetry group of a multipole does not determine its late-time decay rate.Comment: 12 pages, 13 figures, 4 tables. Substantially revised manuscrip