Research

I am interested in the application of General Relativity to modeling astrophysical systems. My main research topic is gravitational wave emission from compact binaries with a particular emphasis on perturbative techniques for modeling extreme- and intermediate-mass-ratio inspirals. I am also interested in other topics such as geodesic motion and ray-tracing in black hole spacetimes as well as more general topics like numerical simulation and computational techniques.

Below is a short overview of my research. My peer reviewed work can be found on my publications page. I will write posts about various aspects of my research as I go along.

Gravitational waves from compact binaries

emri_0 This is the main focus of my research. I use black hole perturbation theory to model compact binary systems where one component is much more massive than the other. When the larger body is a massive black hole the emitted gravitational radiation will be detectable with future space-based detectors, such as eLISA. When one of the bodies is a few hundred solar masses the emitted radiation will be detectable with ground-based interferometric detectors, such as LIGO, VIRGO, KAGRA, etc. The goal is to accurately model the waveforms emitted from small-mass-ratio systems for use in matched filtering algorithms. Achieving sufficiently accurate models requires going beyond the leading-order radiative approximation and including subleading-order conservative corrections to the orbital motion.

A lot of my research has focused on calculating these important subleading-order corrections as part of what is usually called the `self-force’ program. This effort aims to compute the orbital motion of the small body around the larger black hole by calculating the effect of the small body’s interaction with its own metric perturbation. As we usually model the small body as a point particle this involves delicate regularization procedures. This, in turn, necessitates the development of highly accurate numerical codes to calculate the metric perturbation.

The results have been very fruitful. My collaborators and I have calculated the force felt by the smaller body from the self-interaction [1], and the resulting inspiral evolution [2], [3]. We have also introduced new gauge-invariant quantities [4], [5], [6], [7], which have allowed for comparison and synergies with other methods for solving the general relativistic two-body problem [8]. A good part of the research for my PhD involved making the first self-force calculations for orbits in the Kerr spacetime of a rotating black hole [9], [10], [11]. I’ve recently returned to this topic by exploring the gravitational radiation emitted when the black hole is rotating very close to its maximum rate [12], [13].

Finally, all self-force calculations to date have been at first-order-in-the-mass-ratio but it is necessary to go to second-order for the error in the phase of our models to be less than the one radian required for accurate parameter estimation. I am part of an international team working to make the first second-order calculation, and a few papers developing the necessary numerical techniques are already out [14], [15].

Geodesics motion in black hole spacetimes

generic_orbit_3d_corotatingWhen radiation reaction forces are negligible (i.e, in the test particle limit) the smaller body moves along a geodesic of the background black hole spacetime. These geodesics can be very complicated when the central black hole is rotating. Understanding and efficiently computing geodesics is an important part calculating radiation reaction forces in extreme-mass-ratio systems. Geodesic motion is interesting in its own right as well; one of the papers I have enjoyed writing the most was about isofrequency pairing of geodesics. This newly discovered feature of geodesic motion in black hole spacetimes taught us that it is possible to have two physically distinct bound geodesics which share the same orbital frequencies.

X-ray reverberation around accreting black holes

Schwarz_rl_3p1_timing_colorsThis is a recent project to model how x-ray’s created during a flare are reflected and then emitted from a black hole spacetime. Currently writing code to ray-trace and calculate the time of arrival of x-rays reverberating around a black hole with an accretion disk. I’ll make a post about the results and the methods I am using soon.