## Research

My research centers on Black Holes, objects with so strong gravity that nothing can escape, not even light. Black holes and their properties are predicted by Einstein's theory of General Relativity, and my main activity are computer calculations of Einstein's equations to learn about black holes.

 Simulation of inspiral and merger of two non-spinning black holes (in collaboration with Numerical Relativity groups at Caltech and Cornell)

When black holes collide, they emit a prodigious amount of gravitational waves, ripples in space-time itself traveling with the speed of light (gravitational waves are yet another consequence of Einstein's equations). By observing gravitational waves here on Earth, we can learn a lot about the objects that made them. Most importantly (from my view) about black holes, but also about Neutron stars, supernovae, perhaps even gravitational waves from cosmic strings or the big bang itself.

 LIGO gravitational wave observatory (Washington state); illustration of gravitational waves and the planned LISA spacecraft.
Several detectors are already searching for gravitational waves, most notably the LIGO observatory in the US, but also VIRGO and GEO in Europe, and TAMA in Japan. Unfortunately, gravitational waves are very difficult to detect. To make finding the waves easier, it helps to know the shape of the waves (of, e.g. a binary black hole). To figure out what one has seen, one must know the shapes of the waves emitted from different objects (e.g. non-spinning black holes vs. spinning black holes vs. a Neutron star crashing into a black hole), and compare to what has been observed. That's where my research in simulating black holes comes in.

 Domain-decomposition used for the binary black hole evolution.
Because of the complexity of Einstein's equations, such computer simulations require large super-computers to run on, and they require attention to a lot of details. How does one compute the initial conditions from which to start? How does one compute how fast the simulated black holes spin? How does one control the eccentricity of the orbit of the two black holes ("real" black holes in the Universe are expected to orbit about each other on almost perfect circles. So we better simulate such circular binaries, and not highly eccentric ones). The computer simulations must be highly accurate, hence a lot of effort goes into making them accurate, and into ensuring that they are indeed as accurate as we think they are. Our Spectral Einstein Code (SpEC) is probably currently the fastest and most accurate code. It is a multi-domain (see picure) pseudo-spectral method. Nevertheless, I am interested in developing faster and more accurate computational methods.

 Space-time diagramm of a mass-ratio 1:6 BBH simulation. Time flows up in this diagram.
After a numerical simulation is completed, one needs to understand what it means, and what its implication are for data-analysis of the gravitational wave detectors. Questions like: How well do analytical perturbation calculations agree with the numerical simulations? (if paper-and-pencil gives you the answer, there is no need to burn computer time). How well does LIGO see the computed waves? How can we use the computer simulations to make LIGO see farther? (in other words, how can we find weaker signals?) One additional, particularly cool aspect of the research is development of visualization to help understand what is going on in the simulations.