*Note: the content below is now quite old; I have not had time to regularly update this site.*

### Black Holes and Gravitational Waves: a brief introduction

*Gravitational waves* are oscillations in the gravitational field that propagate throughout the universe at the speed of light. They are analogous to the more familiar electromagnetic (EM) waves, which are oscillations of the electric and magnetic fields. While EM waves are produced by the motions of magnets or electric charges, gravitational waves are produced by the motions of masses. The gravitational waves produced in normal situations (such as when you shake your fist back and forth) are far too weak to ever be detectable. However, there are astronomical sources that can produce detectable gravitational waves.
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### Research Motivations

Because the gravitational-wave signals from even the strongest astronomical sources are very weak compared to the noise in the detector, it is necessary to have an accurate model (or template) for the gravitational-wave signal we are trying to measure. Accurate templates allow us to find a weak signal in the noise-dominated detector output. The main theoretical difficulty lies in generating these templates. This usually involves solving Einstein's equations, a complicated system of nonlinear, partial differential equations that describes the gravitational interactions between objects in the general theory of relativity.

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### Research Projects: overview

Below are some brief descriptions of some of the projects that I've worked on. Most of these concern the coalescence of binary compact objects, a key source for LIGO and LISA. To better understand the context of these projects, it is important to understand the

#### » gravitational wave memory

In the usual picture of a gravitational wave signal, the waveform amplitude starts small at early times, grows to some maximum value, and then decays back to zero (see, eg., the black hole cartoon picture in the previous section). But some sources have what's called **gravitational-wave memory**: the gravitational wave signal does not decay back to zero amplitude, but instead asymptotes to some non-zero value at late-times.

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#### » radiation recoil: how black holes get their kicks

As discussed above, gravitational waves carry away energy from a binary system, causing the orbital separation to shrink (decreasing the orbital energy of the binary). In addition to energy, these waves also carry away *linear momentum*. This loss of linear momentum imparts a corresponding change to the momentum of the binary, causing a "recoil" of the center-of-mass of the binary. This effect is similar to the recoil of a gun after it is fired. Amazingly, when two black holes merge the resulting recoil can be large enough to eject the remnant hole from its galaxy or star cluster.
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#### » eccentric binary inspiral

When scientists at LIGO and other ground-based detectors search for gravitational waves from inspiraling compact binaries, the search templates they use usually assume that the binaries' orbits are circular rather than eccentric. This is generally considered to be a good approximation because gravitational-wave emission tends to make binaries more circular — so binaries formed in the standard way are likely to have negligible eccentricity when they enter the LIGO frequency band. However, there are a variety of non-standard scenarios through which the binary eccentricity might be non-negligible. For this reason, it is important to also account for the effects of eccentricity when modeling gravitational-wave sources. Furthermore, eccentricity effects are even more important for gravitational-wave sources that will be observed by LISA. click to read more...

#### » extreme-mass-ratio inspirals

An "extreme-mass-ratio inspiral" (or **EMRI** ) refers to a binary system consisting of a solar-mass star or compact object (most likely a stellar-mass black hole) in a close orbit around a supermassive black hole. Such systems are likely to exist at the centers of most galaxies and one of the key gravitational-wave sources for LISA. EMRIs are especially interesting because the orbit of the compact object (and the corresponding gravitational waves that it emits) acts as a probe of the spacetime geometry of the larger black hole. Measuring the waves from such systems will thus allow us to test how accurately the black holes we observe in nature agree with the simple and precise mathematical solution provided by Einstein's equations.
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#### » gravitomagnetic Love numbers & tidal crushing of neutron stars

When two gravitating bodies are widely separated, their interactions and dynamics can be described by assuming that they are two point particles. But when the objects are "close", we need to worry about finite-size effects: For example, because one side of the Earth is closer to the Moon than the other, the Moon's gravity pulls more strongly on the closer side than on the opposing side. This causes a stretching or *tidal distortion* of the Earth's oceans that results in the twice daily high and low tides (the Earth's surface and interior is also stretched, but not as much). For inspiraling neutron stars and white dwarfs, these tidal interactions can also be important.

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#### » tidal energy transfer in general relativity

One of the projects I worked on as an undergraduate concerned the description of tidal interactions in general relativity. This was part of a SURF summer research project with Kip Thorne. The project was motivated by Thorne's analysis of tidal interactions related to the Wilson-Mathews-Marronetti controversy discussed above; but the main problem can be phrased in a more general context: unlike some other forms of energy, gravitational energy is known to be non-localizable — in some local region one can always transform to a freely falling frame in which the gravitational-field vanishes. How does this non-localizability affect tidal interactions, which clearly can do mechanical work on a system? (For a dramatic example of tidal work, check out the volcanos on Jupiter's moon, Io.)

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*Last updated on January 22, 2011*

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