Theory Meets Data Analysis at Comparable and Extreme Mass Ratios - 2010

Gravitational wave data analysis of compact binary systems requires the use of matched filtering. This technique cross-correlates the data stream with a certain template that characterizes the gravitational wave signal. Successful parameterestimation thus requires an accurate model of the gravitational wave template. In this talk I will describe a new fast and accurate technique to model the gravitational wave signal from extreme-mass ratio inspirals. Such events consisting of a neutron star or solar mass black hole spiraling into a supermassive black hole are staple sources of the Laser Interferometer Space Antenna. This new model combines the effective-one-body formalism of post-Newtonian theory and black hole perturbation theory leading to accurate waveforms both when the supermassive black hole spins and when it does not.

We present a second order perturbative formalism that includeperturbative spin effects and apply it to the computation of recoil velocites of merging binary black holes and to the computation of waveforms from small mass ratio binaries.

Recent numerical simulations of spinning binary black holes have found that the orbital plane tends to bob up and down in phase with the orbit. It will be shown that similar effects occur in nearly all relativistic systems. The reasons for this are essentially kinematic and appear unrelated to those leading to the final "kicks" observed after merger. Simple examples are provided for binary systems bound together by gravitational electromagnetic and mechanical forces.

Black holes play a central role in astrophysics and in physics more generally. Candidate black holes are nearly ubiquitous in nature. They are found in the cores of nearly all galaxies, and appear to have resided there since the earliest cosmic times. They are also found throughout the galactic disk as companions to massive stars. Though these objects are almost certainly black holes, their properties are not very well constrained. We know their masses (often with errors that are factors of a few), and we know that they are dense. In only a handful of cases do we have information about their spins. Gravitational-wave measurements will enable us to rectify this situation. Focusing largely on measurements with the planned space-based detector LISA, I will describe how gravitational-wave measurements will allow us to measure both the masses and spins of black holes with percent-level accuracy even to high redshift, allowing us to track their growth and evolution over cosmic time. I will also describe how a special class of sources will allow us to measure the multipolar structure of candidate black hole spacetimes. This will make it possible to test the no-hair theorem, and thereby to test the hypothesis that black hole candidates are in fact black holes are described by general relativity.

With several ground-based gravitational wave interferometers operating at design sensitivity the need for high-order post-Newtonian (PN) calculations of potentials waveforms etc. especially including spin effects has grown significantly over the last several years. Not only are these calculations necessary for precisely estimating the parameters of detected gravitational wave sources but they are also useful for providing more accurate models of binary evolutions in for example the effective one-body program and for computing the PN contributions to self-force effects in the extreme mass ratio limit. Since these calculations become more demanding to carry out at higher PN orders it is necessary to utilize symbolic computer algebra programs (such as Mathematica). Our aim is to automate PN calculations (of potentials power loss etc.) on the computer using the effective field theory (EFT) approach of Goldberger and Rothstein which is itself a systematic and algorithmic method for computing in the PN approximation. The EFT approach lends itself to automation through definite power counting rules that identify precisely those interactions appearing at a given PN order through Feynman rules and diagrams that provide an elegant way to side-step the need to explicitly solve the wave equation for metric perturbations (unlike in traditional methods) through working at the level of the action (a scalar) instead of equations of motion etc. We discuss our progress in automating these calculations on a computer using the EFT approach.

Recent progress in numerical- and analytical relativity enables us to construct analytical waveform templates coherently describing the inspiral, merger and ring down of coalescing black-hole binaries. Such waveform templates not only improve the sensitivity of the searches for gravitational waves from high-mass binaries significantly, but also the accuracy of the parameter estimation. This talk summarizes the status and prospects of different approaches of the modeling of gravitational waveform from binary black holes calibrated to numerical- relativity simulations.

The initial gold rush of exploration into new regions of parameter space has slowed significantly. While our ability to simulate larger spins and more extreme mass ratios has continued to improve, much of the recent progress in numerical relativity has centered on improvements in methodology, in condensing and interpreting an ever-growing body of numerical results, and in incorporating matter into the numerical simulations. In this review, I will summarize the recent progress in this field, focusing on novel results in the simulation of black hole binaries, with some discussion of novel applications of those results to data analysis.