Research

The Hughes group studies astrophysical applications of Einstein’s general theory of relativity. Much of our work focuses on sources of gravitational waves and the astronomy done with gravitational-wave measurements. In recent years, our efforts have focused in particular on studies of the two-body problem in general relativity using perturbative techniques, and using these studies to learn about the gravitational waves produced by two-body systems (especially systems with two black holes).

The discussion here is not comprehensive, but serves as an illustration of topics that have been important foci of our work, especially in recent years.

The two-body problem via black hole perturbation theory

A fairly simple problem in Newtonian gravity, the two-body problem in general relativity is far more challenging. The core of the challenge is that, in general relativity, one doesn’t so much model “two bodies” as one models a single spacetime which, in appropriate limits, can be regarded as two bodies. This spacetime includes radiation, is governed by coupled nonlinear differential equations, and has boundaries (event horizons) whose locations, in the general problem, cannot be determined until the calculation is complete. Numerical relativity, in a triumph of progress since about 2005, can now model a tremendous range of astrophysically relevant situations.

Much of our work in this area uses black hole perturbation theory (BHPT). The equations of BHPT are simpler than the “full” general relativity field equations solved by numerical relativity, and as such can be solved relatively quickly and with high precision. However, they only work well if a binary can be treated as a perturbation to an exact black hole solution. In practice, this means BHPT can be used to model large mass ratio binaries. The spacetime of this binary is then accurately approximated as the exact solution describing a black hole perturbed by the smaller body, and the binary’s dynamics are described in terms of the dynamics of the perturbation due to the smaller body.

Note: P.I. Hughes is a founding member of the Black Hole Perturbation Toolkit, a consortium which develops and publishes open-source tools for studying the equations of BHPT. This includes at present a constrained version of the P.I.’s C/C++ code for solving the Teukolsky equation (Gremlin). Work is in progress to provide an open-source fully-fledged version of this code, good for generic black hole orbits. Such a code exists, but due to licensing requirements for some of the libraries it uses, the current version cannot be publicly released. The code, or subsets of the code, can be made available to interested colleagues on a case-by-case basis; please inquire of Hughes if you are interested.

Much of this work has been motivated by extreme mass ratio inspirals (“EMRIs”). Astrophysically, these are binaries formed by the capture of a stellar mass compact object captured onto a strong-field orbit of a massive black hole. Such binaries are expected to be important sources for the space-based detector LISA. BHPT is the perfect tool for modeling such binaries; direct calculation of EMRIs using numerical relativity is not currently feasible due to the very large dynamic range in scales that must be resolved in large mass-ratio calculations. Work over the past decade has shown that the large mass-ratio limit also helps to understand aspects of the general case; for example, showing that certain behaviors arise due to beating between frequencies that describe bound black hole orbits, or demonstrating how black hole ringing modes are excited by the final dynamics of a merging binary.

Details of the work our group has done in this area can be found by following the links for Publications, Visualizations, and Sounds.

Gravitational-wave astronomy and astrophysics

Over the years, members of our group have also done significant work on the astronomy that can be done with gravitational-wave measurements, and the astrophysics of strong gravitational-wave generators. Examples of such work include

• With collaborators Daniel Holz and Marc Favata, the first first modern calculations of recoil imparted to a remnant black hole following binary merger (since superseded by numerical relativity ccalculations),

• Foundational work on standard sirens, especially with Holz,

• Many studies in the early days of the LISA mission of how well we can determine the properties of merging black holes (their masses and spins, the position on the sky, their distance from us) from gravitational wave measurements,

• Development of a scheme (the “bumpy” black hole) to map the spacetimes of massive compact objects and test the hypothesis that they are described by general relativity’s Kerr metric.

More recently, members of our group have studied the relativistic dynamics of “hierarchical triple” systems: systems with three objects, two bound into a tight binary which itself either orbits or is orbited by a third body.

We have generally been less active in these topics in recent years, largely because of P.I. Hughes’ time constraints. Gravitational-wave astronomy has moved extremely fast in recent years, and with the P.I. active in MIT departmental leadership and with a young child at home, it is difficult to keep up. However, group members are encouraged to get involved in other activities as their time permits. For example, Hughes is an associate member of the LISA Consortium, though at present not highly involved. Research postdoctoral group member Lionel London is a full member of the LIGO Scientific Collaboration, and was deeply involved in day-to-day LIGO activities during his time as part of the Hughes group.