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Physics 387N

Computational Relativity

Unique Number 53110

TTH 11:00-12:30 RLM 5.118

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Instructor: Richard A. Matzner

Office: RLM 9.208

Phone: 471 5062

## Motivation

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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For questions or comments regarding the class send email to
richard@ricci.ph.utexas.edu