Let us describe why the numerical calculation of quasi-normal
mode frequencies is delicate. Consider again the case treated in
section
2
of the wave equation with a potential with compact support. We
try to find a complex number
s
with negative real part such that the solution which is
for large positive
x, is
for large negative
x
. Note that these solutions grow exponentially with |
x
| and therefore one has to be very careful to make sure that
there is no exponentially decaying part in the solution. The
situation becomes even more complicated if we do not know
explicitly because one can not characterize the correct solution
by some growth property. This is for example the case for the
Schwarzschild solution.
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Quasi-Normal Modes of Stars and Black Holes
Kostas D. Kokkotas and Bernd G. Schmidt http://www.livingreviews.org/lrr-1999-2 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |