Title:         Numerical problems in general relativity

Authors:       Douglas N. Arnold

Source:        in: "Numerical Mathematics and Advanced Applications" (P>
Neittaanmäki, T. Tiihonen, and P. Tarvainen, eds.), World Scientific,
2000, pp. 3-15

Status:        Published

Abstract:  The construction of gravitational wave observatories is one
of the greatest scientific efforts of our time.  As a result, there is
presently a strong need to numerically simulate the emission of
gravitation radiation from massive astronomical events such as black
hole collisions.  This entails the numerical solution of the Einstein
field equations.  We briefly describe the field equations in their
natural setting, namely as statements about the geometry of space time.
Next we describe the complicated system that arises when the field
equations are recast as partial differential equations, and discuss
procedures for deriving from them a more tractable system consisting of
constraint equations to be satisfied by initial data and together with
evolution equations.  We present some applications of modern finite
element technology to the solution of the constraint equations in order
to find initial data relevant to black hole collisions.   We conclude
by enumerating some of the many computational challenges that remain.

Keywords:      general relativity, gravitational radiation, black holes, Einstein equations

Subj. class.:  65N30, 83C05, 83C35, 83C57

URL:           http://ima.umn.edu/~arnold/papers/enumath.pdf