Gravitational Waves

Imagine two ants standing near the edge of a large trampoline. Suppose we measure the two ants to be separated by an inch of fabric. Now imagine that two children decide to sit in the middle of the trampoline. This would distort the fabric of the trampoline such that, if we were to measure the distance between the ants again, we would find that it had increased. This is not because the ants have moved, they are still each standing on the same bits of fabric, but because the fabric itself has been stretched. Now imagine that the children begin to chase each other in circles around the center of the trampoline. As they move, the fabric of the trampoline will expand and contract in response to their motion. These distortions pull on nearby pieces of fabric, which pull on bits of fabric near to them, until eventually these distortions reach the ants. As a result of the distortions, the distance between the ants will increase and decrease in proportion to the speed and separation of the children. Therefore, by measuring the distance between the ants, we can supervise the children.
Physical space behaves a lot like this. As black holes orbit and merge, they create distortions in space which motion out into the universe. These distortions expand and contract space perpendicular to their motion. This is what a gravitational wave is. Here, the children are black holes, and the trampoline is space. What about the ants? Just as we imagined measuring the distance between two ants to supervise children, instruments like LIGO bounce light between far apart mirrors to measure the distance between them and understand the properties of orbiting black holes and other massive moving objects. By comparing LIGO data with numerical simulations, we can learn about the mass, spin, and orbital frequency of black holes and neutron stars. Soon instruments like LISA, Cosmic Explorer, and The Einstein Telescope, will help us detect gravitational waves produced by lazy teenagers who are heavier and don’t have the energy to run quite so fast. This is all important for understanding astrophysical phenomena such as black hole formation. It also allows us to test the accuracy of general relativity by assessing how well simulations using general relativity match data compared to simulations using other theories. Some day these detectors may even identify gravitational waves emitted from as of yet undiscovered particles super radiating around black holes, or help us understand cosmology by detecting gravitational waves produced during the big bang.
Numerical Relativity

The nonlinear, dynamical and strong field regime of gravity that unfolds during the merger of compact objects, such as black holes or neutron stars, may hold the key to understanding the true nature of gravity. However, it can not be modeled analytically. To enhance our theoretical understanding of this regime, we employ full-blown numerical relativity simulations in which we solve the Einstein equations (or extensions thereof) on high-performance computing facilities. We focus on black hole or neutron star mergers in 3+1, classical general relativity, in higher dimensional spacetimes, and in modified theories of gravity. One of the pressing goals of numerical relativity is to calculate gravitational waves from promising astrophysical sources, in order to provide theoretical templates both for ground- and space-based detectors. Pioneering new numerical formulations of general relativity — and other proposed theories of gravitation — and algorithms suitable for stable, numerical solution of both the initial value and constraint equations and the evolution equations are major challenges of numerical relativity. Another challenge is developing reliable physical modeling to describe realistic astrophysical sources of gravity, cementing numerical relativity an essential tool of “multimessenger astronomy”.
Waveform Catalogues

The LVK gravitational-wave observatories have observed ~90 signals as of the end of the third observing run. With the fourth observing run already underway and future detectors anticipated in the coming decade, even more events are expected, with even higher signal-to-noise ratios. These gravitational waves encode information about the merging compact objects that emitted them as well as information about the nature of gravity itself. This information can be decoded using banks of template waveforms generated using numerical relativity. These template waveforms are compared to the observed data, recovering information about the merging objects and the laws of gravity. With the high sensitivity of next-generation observatories, we will be able to use this information to put general relativity to the test and probe additional theories of gravity. Accomplishing these goals will require vast template banks of highly accurate numerical relativity waveforms.
Tests of General Relativity & Modified Gravity

In recent years, Einstein’s theory of General Relativity has been put to the test via astrophysical observations such as gravitational wave detections, shadows of supermassive black holes, and X-ray emission from accretion disks. While Einstein’s theory of General Relativity has passed these tests, it does not give a renormalizable theory of gravity. Thus, we strive to find where general relativity (potentially) breaks down. For example, astrophysical black holes provide a laboratory to test deviations from Einstein’s General Relativity. For instance, no-hair theorems state that black holes in general relativity are parameterized by only three conserved quantities: mass, angular momentum, and electromagnetic charge. Thus, the presence of an additional conserved quantity would violate no-hair theorems and act as a “smoking gun” to indicate that General Relativity has been violated. We consider extensions of General Relativity, commonly referred to as modified theories of gravity, to explore potential violations of no-hair theorems. By implementing modified theories of gravity numerically on supercomputers, we are able to produce numerical waveforms to compare with actual gravitational wave data. This comparison between actual data and numerical waveforms allows the community to test and quantify deviations from General Relativity. Looking towards the future, we eagerly anticipate next generation ground based and space based detectors to further explore potential modifications to General Relativity as we continue to probe more extreme regions of the universe.
Cosmology
Everything that we can touch and see, including ourselves, consists of atoms that were once generated within some star. It is only natural that we want to know what lies beyond the horizon of our Universe. We develop technologies and theories to satisfy that insatiable curiosity.

Einstein’s theory of gravity gave birth to the field of cosmology, which spans the birth of the Universe 13.7 billion years ago to the far future, including all the galaxies and everything else we can see in between. Cosmology plays a crucial role in both the formation of supermassive black holes and the dynamics of dark matter in clusters and halos. Furthermore, the early stages of the Universe’s evolution are responsible for the generation of all existing elementary particles, marking the point where cosmology intersects with particle and high-energy physics.
With the advent of gravitational wave observations, a new epoch in the study of cosmology has begun. Current gravitational wave observations can refine information about the rate of expansion of the Universe through precise and independent measurements of the Hubble constant. Future gravitational wave observations with second-generation detectors may even provide information about the dark energy equation of state, which relates the pressure and density of a dark energy fluid. Third-generation detectors may also detect or place constraints on a cosmological stochastic background of gravitational waves produced in the early Universe through phase transitions or topological defects.
We work on modeling these phase transitions, topological defects, and other cosmological effects on gravitationally bound systems, particularly on the gravitational waves emitted by binary systems. Finally, we are able to compare these models to data to extract cosmological information.
Black Holes as Laboratories for Particle Physics

While we have a good understanding of the ordinary matter that forms our everyday world, 83 % of the matter in the universe still can not be explained by our best description of the fundamental particles, the Standard Model. The nature of this “dark matter” has remained the greatest mystery in modern physics for the last several decades, and little is known about its composition or origin aside from its gravitational imprint on the cosmos. A large number of models have been proposed to explain the nature of dark matter, but so far it has slipped past all our experimental efforts to reveal its identity. Black holes, being one of the most extreme environments in the universe, may just be the right testing ground to shed light on certain dark matter candidates. The key to this is the process known as “superradiance”: If dark matter were composed of bosonic fields, then it could be amplified around a rapidly rotating black hole, forming macroscopic clouds that extract energy and angular momentum from the black hole. This effect would cause the black holes to spin down. Consequently, the expected depletion of high spin black holes allows us to place constraints on bosonic dark matter candidates by analyzing statistics on black hole populations. Furthermore, their dynamics around black holes is enriched in the presence of a second black hole: the bosonic cloud, similar to a hydrogen atom, has energy levels which can undergo transitions and resonances when perturbed by the binary companion. As the binary spirals and comes to a merger, these interactions can lead to sharp, observable impacts on the binary dynamics, as well as gravitational wave emission. With the field of gravitational wave astronomy rapidly advancing, we are entering a new era to test fundamental physics with observations, and numerical relativity is our theoretical laboratory best suited to probe new physics in this highly nonlinear regime of gravity.
Superradiance

If you jump onto a spinning merry-go-round and then jump off again, you will find that when you jump off you are moving much faster and have much more kinetic energy than you began with. If you ever foolishly tried this as a child, you quite likely hurt yourself. (Please, please, do not try this, anywhere). Simultaneously, when you did this the merry go round would have lost the same amount of energy that you gained in the process. This phenomenon, broadly speaking, is called Superradiance.
As it turns out, a spinning black hole acts a lot like a merry go round. As a black hole spins it quite literally drags space around it, which forces anything that comes near to the black hole to rotate with it. So, if something gets very near to a spinning blackhole, it can gain energy from the blackhole by throwing something into the black hole in such a way that it decreases the black hole’s energy. This is known as the Penrose Process (Penrose & Floyd 1971). A similar, but different process can occur around non-spinning black holes with an electric charge. It just so happens that one can imagine many different scenarios where particles, magnetic fields, or even gravitational waves might get very close to such a black hole, and spontaneously extract energy from it. For example, many hypothetical particles should form clouds around black holes a bit like how electrons do around an atom. As a result these particles would gain energy, and ultimately lead to the spontaneous production of more particles. This phenomena appears in numerous different areas of active research such as theories of quantum gravity, dark matter candidates, the production of relativistic jets, and many more discussed elsewhere on this page (see Superradiance by Brito et al. 2015).