# Major projects and research directions

Here we describe some of the major directions that are being pursued in our group. This list is

*not*intended to be exhaustive, but is intended to illustrate some of the most active or productive directions we have been following lately.

### The two-body problem via black hole perturbation theory

Although a well-known and fairly simple problem in Newtonian gravity, the two-body problem in general relativity is quite a tough nut to crack. Most of the issues can be traced back to the fact that, in general relativity, one doesn't so much model "two bodies" as one models a single spacetime that, in appropriate limits, can be regarded as two bodies.

Much of our work is based on using black hole perturbation theory to understand this problem. If one body is much more massive than the other, then the spacetime of the binary is approximately that of the larger body (which we take to be that of a black hole), perturbed by the smaller body. The binary's dynamics can then be described in terms of the dynamics of the perturbation due to the smaller body.

We have developed two codes for modeling the evolution of this perturbation; both are based on Saul Teukolsky's 1973 equation describing the evolution of radiative curvature perturbations to rotating black holes. One code works in the frequency domain, decomposing the perturbation into harmonics of the orbital frequencies characterizing black hole orbits. The other works in the time domain, evolving the perturbation directly as a 2+1 dimensional partial differential equation on a numerical grid. Both codes have strengths and weaknesses; the combination of the two allows us to use both tools in concert in a way that emphasizes their strengths.

Past work has largely been motivated by the

*extreme mass ratio inspiral*, or "EMRI," problem, modeling the dynamics and gravitational waves generated by a small object captured and spiraling into massive black holes. Though EMRI issues are still of interest, future work is likely to focus on the issue of modeling binary black holes more generally. We have become particularly interested in using perturbation theory as a high precision tool for studying a limiting case of the binary black hole, and plan to study how these tools can provide input to numerical modeling of binary spacetimes and the effective one-body approach to binary dynamics.

Former students Steve Drasco, Marc Favata, and Pranesh Sundararajan have worked on this problem, as has former postdoc Joel Franklin. Currently, UROP student William Throwe is pursuing aspects of this problem.

### Mapping the spacetimes of massive compact objects and testing the black hole hypothesis

Extremely massive and compact concentrations of mass are found in various configurations in our galaxy and in the universe. By now, the most conservative explanation explaining these objects is that they are black holes. Accepted physics does not include any other configuration of matter which is stable on these time scales

*and*is as massive and compact as needed to explain the data.

Are they black holes? What if effects beyond known, accepted physics give us some configuration that can explain these observations without being the black holes that are predicted by general relativity? The question then becomes

*What observations can be done to establish firmly that these objects are, in fact, the black holes of general relativity?*

Answering this means that we must establish experimentally that black hole "candidates" have the unique characteristics predicted of black holes. One excellent line of reasoning being pursued by colleagues at other institutions is to establish that these objects have

*event horizons*: One way surfaces through which light and matter can enter, but from which they cannot come out. A similar approach is followed in work to map in radio the nature of the massive object at the core of our galaxy.

The approach we are pursuing is based on the "No hair" theorem of general relativity: A true black hole's external spacetime is

*uniquely*determined by the hole's mass and spin. Once those two numbers are known, the geometry is

*completely*specified if it is a black hole. The formulation we use is based on a multipolar description of the spacetime. A black hole can be described by a set of multipole moments which describe how its gravitational interaction varies with distance and position.

*If*the black hole candidate is a black hole in general relativity, then once two of those moments are known,

**of the remaining ones are specified. General relativity gives us no freedom to adjust those moments beyond the choice of the hole's mass and spin. We suggest "mapping" the strong field spacetime by measuring the multipole moments which characterizes it.**

*all*What's attractive about this approach is that it can be formulated as a

*null experiment*. The null hypothesis is that black hole candidates are the black holes of general relativity; testing it requires a framework for studying objects that have a multipolar structure more general than this. Working with Hughes, former student Nathan Collins introduced the "bumpy black hole," a nearly-black-hole object with the "wrong" multipole moments, but that includes GR's black holes as a limit. Current student Sarah Vigeland has taken this starting point and run with it, improving the mathematical description of a spacetime's "bumps," improving the description of orbits and motion in these spacetimes, and extending the original Collins & Hughes work to encompass bumpy black holes with spin.

### Assessing the science reach of space-based gravitational-wave detectors

Much of our group's work is related to the science that can be done when we are able to regularly measure gravitational waves (GWs) from astronomical sources. Related to this, Hughes is a member of the International Science Team for LISA, the Laser Interferometer Space Antenna. This is a planned space-based antenna for measuring GWs from violent astrophysical events.

A substantial portion of the work we have done in the past few years has had as its goal understanding the capability of LISA to provide astronomically useful information about GW sources. With Ryan Lang, we have focused in particular on how well LISA can measure the properties of merging black holes. We modeled binary dynamics including the full impact of precession due to interactions between the black holes' spins. These precessions modulate the gravitational waveform in both amplitude and frequency; we showed that these modulations break parameter degeneracies and greatly aid our ability to measure a binary's properties.

Stephen O'Sullivan is continuing to pursue aspects of this work. In addition, we are collaborating with Neil Cornish to extend the waveform models used in our analyses, as well as to improve the analysis which underlies our estimation of parameter measurement accuracy.

### Multimessenger astronomy using gravitational waves

GWs arise from violent astronomical events. Many of these events will be accompanied by other forms of radiation. For example, the coalescence of two neutron stars is likely to be accompanied by a gamma ray burst. Combined observation of these events in both GWs and other channels is sure to greatly increase what we can learn from their observation.

Largely led by former postdoc Samaya Nissanke, we have examined how well, by combining GW and electromagnetic observations of short gamma ray bursts, we might be able to pin down the distance to the source. By combining these measurements with an electromagnetic determination of the source's redshift, we can then --- in principle --- make a calibration-free measurement of the Hubble constant. In practice, it will take a

*lot*of high signal-to-noise measurements to be able to measurement Hubble with interesting precision. We also find that such measurements will require a rather broad network of advanced ground-based GW detectors --- not just the two LIGO instruments, but also Virgo in Europe and (ideally) proposed instruments in Australia and Japan.

### "Optimally" configuring advanced detectors

The sensitivity of advanced ground-based GW detectors will be, to some extent, configurable. This means that the noise curve of these instruments can be shaped so as to "optimally" measure the characteristics of sources.

What does "optimally" mean? Answering this question requires us to understand something about the waves we hope to measure, and what what we hope to learn from them. One approach is to assume that the waves are characterized by a parameter of some kind, and to design the sensitivity so that this parameter is measured as well as possible. With Leo Stein, we are examining how well this can be done if our goal is to measure GWs from the late stages of binary neutron star coalescence. At the crudest level, our goal is to update an older analysis by Hughes with more modern and up-to-date descriptions of the detectors. However, Leo has also significantly improved Hughes' original analysis, finding an error in the code that was used in the 2002 paper, and improving the method of extremizing a distribution which assess the quality of measurement. Sadly, the punchline is that our earlier analysis about the late inspiral of binary neutron star coalescence was too optimistic, though tunable advanced interferometers will have significant capability to teach us about these systems and their waves.