# Research Projects

The MSU Relativity, Gravitation and Cosmology group concentrates on undergraduate and graduate education, public outreach and research supported both by NASA and NSF. Our research includes gravitation, relativity theory and data analysis. We collaborate with a variety of institutions in North America, such as CalTech, MIT, Harvard and Princeton University in the United States, as well as the Perimeter Institute in Canada. We also collaborate with institutions in Europe, such as the Cambridge University in England and the Institute d'Astrophysique de Paris in France. We concentrate on the following major areas of study:

- Gravitational Wave Theory
- Gravitational Wave Data Analysis
- Black Hole Theory
- Experimental Relativity
- Cosmology
- Beyond Einstein

## Gravitational Wave Theory

Einstein's theory of General Relativity predicts that accelerating massive bodies will produce gravitational waves, vibrations in the fabric of spacetime. Gravitational wave interferometers in the United States [Laser Interferomer Gravitational Observatory (LIGO)], India (LIGO-India), Italy (Virgo), Germany (GEO) and Japan (KAGRA) will detect such waves before 2020. Space-borne detectors, such as the Laser Interferometer Space Antenna (LISA) mission, are also being planned by both NASA and the European Space Agency. The detection of gravitational waves requires their precise theoretical modeling to allow for the construction of waveform templates with which to filter the noise data.

Our group focuses on the analytical modeling of gravitational waves emitted during the inspiral and merger of compact objects, such as black holes and neutron stars. Such modeling requires the solution to the Einstein equations, which we perform analytically via mathematical series techniques. During the inspiral, when the compact objects have small velocities relative to the speed of light, we employ post-Minkowskian and post-Newtonian techniques to solve the Einstein equations. After the merger, as the remnant compact object settles down to its final stationary state, we employ black hole perturbation theory to solve the field equations. These solutions then allow us to predict the gravitational wave observable from which to construct template filters.

Some of the results of our group efforts can be found below. The LISA calculator provides an approximate gravitational waveform template, while the LISA simulator provides the response of LISA to an arbitrary gravitational wave signal.

## Gravitational Wave Data Analysis

Gravitational waves are incredibly weak. This means that they can propagate essentially unimpeded from large cosmological distance to Earth. But at the same time, this also means that their effect on matter is very subtle. Given a photon that travels down a long 4 km tube, gravitational waves change the distance traveled by less than one part in a thousand of the radius of a proton. Such insanely small distances can only be proved with interferometry. But even then, the interferometric data is mostly polluted by instrumental noise, with possible gravitational wave signals deeply buried in the noise.

Our group develops and implements sophisticated data analysis and statistical techniques to extract gravitational wave information from such noise data streams. If the noise possesses a certain number of properties, template filters are the optimal way to extract such information. But once a detection is made, the estimation of parameters, selection of theoretical models and testing of hypothesis is best carried out with Bayesian techniques. The latter starts by assuming some prior information on the signal and then it uses the data to update this prior. Given a gravitational wave signal buried in the noise, the posterior knowledge obtained through such techniques then immediately leads to a distribution of detected astrophysical parameters and the likelihood that a particular model is preferred by the data.

The Gravity group is a member of the LIGO Scientific Collaboration (ground-based detector) and the LISA Science Team (space-based detector).

## Black Hole Theory

Black holes are perhaps one of the most fascinating predictions of Einstein's theory. These objects are completely gravitationally collapsed objects with such immense gravitational fields that not even light can escape its pull. Within General Relativity, the two most famous black hole solutions were discovered by Schwarzschild and by Kerr and they represent non-spinning and spinning black holes in isolation respectively. But black holes, like any other object in the Universe, does not exist in isolation. These objects are in constant interactions with matter and with gravitational fields from other stars in its surrounding. Such interactions perturb the Schwarzschild and Kerr solutions, inducing dynamics that tidally heat and torque the perturbed black hole.

Our group uses black hole perturbation theory to study such dynamical environments and determine how the mass, angular momentum, surface area and spacetime metric of Schwarzschild and Kerr black holes are affected by perturbing forces. These perturbations are important because they affect the gravitational waves emitted when two black holes inspiral. Any one black hole in a binary is constantly being perturbed by its companion, tidally torquing and heating it, which then translates to modifications in their orbital motion and the gravitational waves emitted.

Once a perturbed black hole spacetime metric is obtained, one can use it to find the dynamical spacetime metric of a binary system. This is achieved by asymptotically matching the perturbed solution valid close to either binary component to a post-Newtonian metric valid sufficiently far away from either companion. These two metrics have overlapping regions of validity, inside which they can be related through certain multiple scale analysis techniques. Once a global dynamical metric is obtained, this can be used as initial data for numerical simulations, or as a dynamical background in which to study certain astrophysical processes, such as accretion in thin disks.

## Experimental Relativity

Einstein's theory of General Relativity has passed all tests we have subjected it to with flying colors. These tests, however, verify Einstein's theory in a regime of spacetime where gravitational fields are rather weak or non-dynamical and speeds are small relative to the speed of light. For example, the gravitational field on the surface of the Earth, or in orbit around Earth, is a million times weaker than close to a black hole. This is why for most tests of General Relativity carried out to date one need only consider the first few terms in a post-Newtonian expansion, neglecting any higher-order non-linearities. On the other hand, gravitational wave observations of the late inspiral and merger of black holes should provide unparalleled information about General Relativity in this strong-field regime.

Our group focuses on understanding what types of tests of General Relativity can be carried out with future gravitational wave observations. An appealing avenue is to consider tests of Einstein's theory that search for generic, model-independent deviations in the data. This allows us to lift any theoretical bias that a particular competing gravitational theory is particularly probably, and instead, allow the data to select whether a deviation is present. Such a model is analogous to current experimental techniques used when analyzing data from binary pulsars and Solar System observations.

## Cosmology

Not only did Einstein's theory reshape astrophysics, but it also gave birth to the field of cosmology, the study of the evolution of the Universe. Cosmology is another exciting area of research with new data coming in from the Plank satellite that show the earliest images of our Universe's birth. Such data and future, planned experiments, will allow us to determine the fundamental properties of the cosmic microwave background to unprecedented levels. Gravitational wave detectors themselves might also be able to provide cosmological information through the detection of stochastic backgrounds.

## Beyond Einstein

General Relativity and Quantum Mechanics are known to be incompatible. A unified theory that is complete and well-posed, however, is still absent. Several quantum gravitational models have been proposed, such as string theory and loop quantum gravity, but none of his is yet in a complete state of development. Lacking a concrete and complete model, it may be interesting to study particular effective theories that modify General Relativity by violating one of its fundamental principles, such as parity invariance, locality, or general covariance.

Our group has been studying a particular class of effective theories that break parity invariance to determine how observables are modified. Parity invariance is a fundamental symmetry that states that the laws of physics are the same no matter whether one uses a left- or a right-handed coordinate system. The standard model of elementary particles, however, is known to include parity-violating interactions, which have already been measured in particle accelerators. The inclusion of parity-violating interactions in the gravitational sector induces a plethora of effects that have interesting observational consequences, such as modifications to the dragging of inertial frames and the rate of inspiral of compact objects.

*Updated: September 2, 2014 15:22*