Wolfgang Tichy

Numerical simulation of orbiting black holes

One of the fundamental problems of general relativity is the two body problem of black holes in orbit. Since in general relativity two orbiting bodies emit gravitational waves that carry away energy and momentum from the system, the two black holes spiral inward and eventually merge. The last few orbits of a black hole binary fall into the strongly dynamic and non-linear regime of general relativity, and we therefore turn to numerical simulations to solve the full Einstein equations. Such numerical simulations have seen many advances in the last few years, but until recently it has not been possible to simulate even a single binary black hole orbit.

Together with Bernd Bruegmann and Nina Jansen at the Institute for Gravitational Physics and Geometry at Penn State University I have developed coordinate conditions which lead to approximately comoving coordinates. Such coordinate systems have the advantage that the rapid orbiting motion of the two black holes is transformed away. The fact that the two black holes do not move with respect to these coordinates simplifies the numerical simulation and also leads to more stable simulations. We are now able to simulate the binary black hole system for slightly more than one orbital timescale. The picture shows the horizons of the two black holes after they have evolved for one orbital timescale. Note that in the coordinates used the two black holes have not moved from their initial positions. Their horizons, however, have been deformed during this time from coordinate spheres into an oblate shape.

Acknowledgments:
This research has been conducted at the Institute for Gravitational Physics and Geometry at Penn State University.