The Collision of Two Black Holes

We study the head-on collision of two equal mass, nonrotating black holes. We consider a range of cases from holes surrounded by a common horizon to holes initially separated by about $20M$, where $M$ is the mass of each hole. We determine the waveforms and energies radiated for both the $\ell = 2$ and $\ell=4$ waves resulting from the collision. In all cases studied the normal modes of the final black hole dominate the spectrum. We also estimate analytically the total gravitational radiation emitted, taking into account the tidal heating of horizons using the membrane paradigm, and other effects. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem, and we find excellent agreement.Comment: 14 pages, 93-

Artifact Rejection Methodology Enables Continuous, Noninvasive Measurement of Gastric Myoelectric Activity in Ambulatory Subjects.

The increasing prevalence of functional and motility gastrointestinal (GI) disorders is at odds with bottlenecks in their diagnosis, treatment, and follow-up. Lack of noninvasive approaches means that only specialized centers can perform objective assessment procedures. Abnormal GI muscular activity, which is coordinated by electrical slow-waves, may play a key role in symptoms. As such, the electrogastrogram (EGG), a noninvasive means to continuously monitor gastric electrical activity, can be used to inform diagnoses over broader populations. However, it is seldom used due to technical issues: inconsistent results from single-channel measurements and signal artifacts that make interpretation difficult and limit prolonged monitoring. Here, we overcome these limitations with a wearable multi-channel system and artifact removal signal processing methods. Our approach yields an increase of 0.56 in the mean correlation coefficient between EGG and the clinical "gold standard", gastric manometry, across 11 subjects (p < 0.001). We also demonstrate this system's usage for ambulatory monitoring, which reveals myoelectric dynamics in response to meals akin to gastric emptying patterns and circadian-related oscillations. Our approach is noninvasive, easy to administer, and has promise to widen the scope of populations with GI disorders for which clinicians can screen patients, diagnose disorders, and refine treatments objectively

User evaluation of an interactive learning framework for single-arm and dual-arm robots

The final publication is available at link.springer.comSocial robots are expected to adapt to their users and, like their human counterparts, learn from the interaction. In our previous work, we proposed an interactive learning framework that enables a user to intervene and modify a segment of the robot arm trajectory. The framework uses gesture teleoperation and reinforcement learning to learn new motions. In the current work, we compared the user experience with the proposed framework implemented on the single-arm and dual-arm Barrett’s 7-DOF WAM robots equipped with a Microsoft Kinect camera for user tracking and gesture recognition. User performance and workload were measured in a series of trials with two groups of 6 participants using two robot settings in different order for counterbalancing. The experimental results showed that, for the same task, users required less time and produced shorter robot trajectories with the single-arm robot than with the dual-arm robot. The results also showed that the users who performed the task with the single-arm robot first experienced considerably less workload in performing the task with the dual-arm robot while achieving a higher task success rate in a shorter time.Peer ReviewedPostprint (author's final draft

New Coordinate Systems for Axisymmetric Black Hole Collisions

We describe a numerical grid generating procedure to construct new classes of orthogonal coordinate systems that are specially adapted to binary black hole spacetimes. The new coordinates offer an alternative approach to the conventional \v{C}ade\v{z} coordinates, in addition to providing a potentially more stable and flexible platform to extend previous calculations of binary black hole collisions.Comment: 3 pages, 5 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

The Head-On Collision of Two Equal Mass Black Holes Peter Anninos

We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about $20M$, where $M$ is the mass of a single black hole. We have extracted both $\ell = 2$ and $\ell=4$ gravitational waveforms resulting from the collision. The normal modes of the final black hole dominate the spectrum in all cases studied. The total energy radiated is computed using several independent methods, and is typically less than $0.002 M$. We also discuss an analytic approach to estimate the total gravitational radiation emitted in the collision by generalizing point particle dynamics to account for the finite size and internal dynamics of the two black holes. The effects of the tidal deformations of the horizons are analysed using the membrane paradigm of black holes. We find excellent agreement between the numerical results and the analytic estimates.Comment: 33 pages, NCSA 94-048, WUGRAV-94-

Asymptotic quasinormal modes of a coupled scalar field in the Gibbons-Maeda dilaton spacetime

Adopting the monodromy technique devised by Motl and Neitzke, we investigate analytically the asymptotic quasinormal frequencies of a coupled scalar field in the Gibbons-Maeda dilaton spacetime. We find that it is described by $e^{\beta \omega}=-[1+2\cos{(\frac{\sqrt{2\xi+1}}{2} \pi)}]-e^{-\beta_I \omega}[2+2\cos{(\frac{\sqrt{2\xi+1}}{2}\pi)}]$, which depends on the structure parameters of the background spacetime and on the coupling between the scalar and gravitational fields. As the parameters $\xi$ and $\beta_I$ tend to zero, the real parts of the asymptotic quasinormal frequencies becomes $T_H\ln{3}$, which is consistent with Hod's conjecture. When $\xi={91/18}$, the formula becomes that of the Reissner-Nordstr\"{o}m spacetime.Comment: 6 pages, 1 figur

New Formalism for Numerical Relativity

We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal slicing, making it potentially very useful for numerical relativity. This development permits the application to the Einstein equations of advanced numerical methods developed to solve the fluid dynamic equations, {\em without} overly restricting the time slicing, for the first time. The full set of characteristic fields and speeds is explicitly given.Comment: uucompresed PS file. 4 pages including 1 figure. Revised version adds a figure showing a comparison between the standard ADM approach and the new formulation. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Appeared in Physical Review Letters 75, 600 (1995

Stuffed Black Holes

Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric is the vacuum solution obtained by the well known conformal imaging method. The interior metric for every black hole is regular everywhere and corresponds to a positive energy density. The resulting matched solutions cover then the whole initial (Cauchy) hypersurface, without any singularity, and can be useful for numerical applications. The simpler cases of one black hole (Schwarzschild data) or two identical black holes (Misner data) are explicitly solved. A procedure for extending this construction to the multiple black hole case is also given, and it is shown to work for all time symmetric vacuum solutions obtained by the conformal imaging method. The numerical evolution of one such 'stuffed' black hole is compared with that of a pure vacuum or 'plain' black hole in the spherically symmetric case.Comment: 12 pages, Latex, 4 postscript figures, corrected some typos, new section about physical interpretatio

Towards a Singularity-Proof Scheme in Numerical Relativity

Progress in numerical relativity has been hindered for 30 years because of the difficulties of avoiding spacetime singularities in numerical evolution. We propose a scheme which excises a region inside an apparent horizon containing the singularity. Two major ingredients of the scheme are the use of a horizon-locking coordinate and a finite differencing which respects the causal structure of the spacetime. Encouraging results of the scheme in the spherical collapse case are given.Comment: 9 page