Physics 387N
Computational Relativity
Unique Number 53110
TTH 11:00-12:30 RLM 5.118

Instructor: Richard A. Matzner
Office: RLM 9.208
Phone: 471 5062


One of the most important problems of classical astrophysical relativity is to understand the behavior of black holes and their interaction. This is very important for the computation of predicted waveforms for the gravitational wave detectors LIGO (US), VIRGO (France/Italy), GEO (Britain/Gemany) currently in construction or in design. Accurate determination of the waveforms will dramatically enhance the design sensitivity of the detectors. Black holes have the strongest possible gravitational fields, and thus their interactions may provide the strongest source of gravitational radiation.

Isolated black holes can be understood from a completely analytical viewpoint. They are axisymmetric (or spherical) objects which are determined completely by specifying their mass, angular momentum, and electric charge. However, interacting black holes are dynamical, typically 3D systems, and the full complexity of the Einstein equations must be used. For this regime, computational approaches are the only feasible choice.

The treatment of black holes on a computer involves a number of different sub-problems. One of the currently outstanding such sub-problems is to handle the computational boundary at the black-hole surface.

The surface of a black hole is the boundary between the external world we can see, and the part of the inside of the black hole that is forever hidden to us. Because the boundary is defined by those light rays just balanced between escape and capture, the horizon has many features of an outgoing shell of radiation. The computational problem then becomes to handle the boundary which is moving at the wave speed (for generality, faster than the wave speed). This problem has proven very difficult in practice.

In this class we will start from very simple wave problems, and progress toward implementing and testing some proposed computational solutions to this problem. Successful results may lead to publication in conference proceedings or in a technical journal.

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