This award supports an integrated program of training and research in gravitational physics, with a focus on the astrophysics of gravitational-wave sources and sources of very strong gravity. This program is designed to prepare for upcoming observations by advanced ground-based gravitational-wave detectors as well as other planned astronomical measurements of strong-gravity systems. It also complements computer simulations of very-strong-gravity binary systems such as black holes orbiting each other. The research supported by this award will have three major components: (1) Studies of black hole perturbation theory (i.e., what happens when the space-time of a black hole is slightly modified), with a focus on how this theory can be used to refine and extend an existing method for modeling strong-field binary systems called the "extended one-body" approach. (2) Astronomy with advanced ground-base gravitational-wave detectors. (3) Testing ideas that will allow assessment of whether astrophysical black hole candidates are truly the black holes of general relativity. The bulk of the work in these research projects will be performed by graduate students, with an important contribution from undergraduates.
This work will help ensure that gravitational-wave detectors reach their full potential as gravitational-wave observatories, opening a new field of observational astronomy. It will also help develop the foundations for probing strong gravity with other astronomical facilities that are under development. This award will support the continued development of a catalog of sounds and videos describing gravitational-wave science, available at the URL http://gmunu.mit.edu. This catalog informs the broader scientific community about the promise of gravitational-wave science, and is an effective public outreach tool. Scientists trained in gravity and gravitational-wave science typically develop a broad range of skills, making them valuable members of the scientific community.
This award continued support for our research group's study of strong-gravity astrophysical systems in general relativity. Much of our work focused on applying black hole perturbation theory (BHPT) to binary systems. We model the binary as a small body orbiting a massive black hole. The binary's dynamics can be modeled as due to a perturbation from the small body to the exact black hole spacetime. Several projects were the focus of our BHPT studies: * Connecting the effective one-body (EOB) approach to BHPT. EOB is an analytic technique for modeling binary systems in general relativity by mapping certain quantities describing the binary into a description of a small body moving in an "effective" spacetime. It has proven to be quite effective at modeling binaries, often reproducing the waveforms predicted by numerical simulations with far less computational cost. EOB requires as input certain quantities that must be taken from detailed binary models. Working with Alessandra Buonanno at the University of Maryland (one of the world's leaders in developing EOB), we used BHPT to provide this input. This has proven very effective at refining the EOB model of how gravitational waves take energy from the binary's orbit, for example, including absorption by the black hole's event horizon, and improving our understanding of how the flux function behaves deep in the strong field. * Orbital resonances: Moments in a binary's evolution when its orbital frequencies are related to one another by a small integer ratio. In Newtonian gravity, a binary is described by a single frequency, which is related to the binary's semi-major axis. This is Kepler's third law of planetary motion. In general relativity, spacetime curvature and frame dragging due to black hole rotation split this frequency into three distinct frequencies in a manner similar to how a magnetic field splits the frequencies of atomic lines into distinct transition levels. When those frequencies are in a small integer ratio (e.g., when the frequency of polar oscillations, Omega_theta, is exactly 3/2 frequency of radial oscillations, Omega_r), then the orbit's evolution can change significantly. Certain components of the self interaction which normally oscillate instead combine coherently. We have shown that resonances are generic: every large mass-ratio system will experience at least one resonance. We also show that when an binary is close to a resonance, it significantly changes the system's evolution. Resonances will shift the system's evolution enough to seriously complicate attempts to measure gravitational waves from large mass ratio binaries. * Tidal distortions of black holes. Much work in recent years has examined how a compact body's shape is changed by tidal forces, with particularly important work focusing on the impact on neutron stars and non-rotating black holes. We have developed a formalism that allows one to similarly study the geometry of a tidally deformed rotating black hole, with no restrictions on black hole spin or the orbit. We only require the binary's mass ratio to be large in order that perturbative techniques are accurate. As a first application, we examined the geometry associated with tides from circular and equatorial orbits. We include two images showing the black hole's horizon for some example orbits. The first shows a slowly rotating black hole distorted by a distant orbiting body; we see a fairly gentle bar-like distortion to the black hole's shape. The second shows a much more extreme distortion for a rapidly rotating black hole with a very close orbiting companion. We will continue this work under this grant's successor, eventually linking it to numerical relativity studies of deformed black holes. We also studied astronomical measurements of strong-gravity objects. In one study, we concluded (rather disappointingly) that plans to test the black-hole nature of massive compact objects were far more difficult than originally thought. Definitively demonstrating that an object is a black hole according to general relativity requires that we have some way of testing its spacetime structure deep in the strong field. It has proven to be extremely difficult to build a well-behaved spacetime that would allow us to test the black hole hypothesis. The most well-behaved spacetimes are in fact the black hole spacetimes themselves --- the very objects we wish to test. We also examined how well gravitational wave measurements of merging compact binaries, when combined with "normal" astronomical telescopes, can be used to measure the expansion of the universe, quantifying how well such a measurement can be done as a function of the number of events measured and the quality of the gravitational-wave antenna network. Four graduate students were trained using funds from this award, two of whom have defended their Ph.D. theses and moved to postdoctoral positions. The other two remain working with our group at MIT (supported by this grant's successor), and will defend their theses in the next calendar year.
