A Computer Algebra Approach

I - The Schwarzschild Spacetime

by

George Davies

Department of Physics and Astronomy

Queen's University, Kingston, Ontario K7L 3N6, Canada

davies@astro.queensu.ca

This example outlines a derivation of the second order perturbations to a
Schwarzschild black hole, highlighting the use of, and necessary reliance on,
computer algebra. The particular perturbation scenario that is presented here
is the case of the linear quadrapole seeding the second order quadrapole. This
problem amounts to finding the second order Zerilli wave equation, and in
particular the effective source term due to the linear quadrapole. With one
minor exception, our calculations confirm the earlier findings of
Gleiser * et. al. *(Gleiser R.J., Nicasio C.O., Price R.H., and, Pullin J., 1996,
*Class. Quantum Grav.*, **13**, L117). On route to these results we also illustrate
that, with the aid of computer algebra, the linear Schwarzschild problem can be
solved in a very direct manner (*i.e.*, without resorting to the usual function
transformations), and it is this ``direct method'' that drives the higher order
perturbation analysis.
The calculations were performed using the GRTensorII computer
algebra package, running on the Maple V platform, along with
new Maple routines that we have written specifically for these types of
problems. Although we have chosen to consider only the
``quadrapole-quadrapole'' calculation in this article, the GRTensor
environment, with the inclusion of these new routines, would allow this
analysis to be repeated for a far more general problem.

- Download paper:
**Fast**, gr-qc/9810056**Fast**, in postscript form blackholes.ps.gz (103 KB)**Slow**, paper in right frame

- Appendix B mws || html
- Entire calculation mws || html
- Dowload the utilities pertutils.mpl

This will appear on the right. Highlite and save the file in the Lib subdirectory of GRTensorII for MapleV Release 5. - Dowload the input files lpschw.mpl and qschw.mpl

These will appear on the right. Highlite and save these in your metrics directory for GRTensorII.

Last update: June 1999