ausblenden:
Schlagwörter:
General Relativity and Quantum Cosmology, gr-qc,Quantum Physics, quant-ph
Zusammenfassung:
It is known that the spectrum of quasi-normal modes of potential barriers is
related to the spectrum of bound states of the corresponding potential wells.
This property has been widely used to compute black hole quasi-normal modes,
but it is limited to a few "approximate" potentials with certain transformation
properties for which the spectrum of bound states must be known analytically.
In this work we circumvent this limitation by proposing an approach that allows
one to make use of potentials with similar transformation properties, but where
the spectrum of bound states can also be computed numerically. Because the
numerical calculation of bound states is usually more stable than the direct
computation of the corresponding quasi-normal modes, the new approach is also
interesting from a technical point of view. We apply the method to different
potentials, including the P\"oschl-Teller potential for which all steps can be
understood analytically, as well as potentials for which we are not aware of
analytic results but provide independent numerical results for comparison. As a
canonical test, all potentials are chosen to match the Regge-Wheeler potential
of axial perturbations of the Schwarzschild black hole. We find that the new
approximate potentials are more suitable to approximate the exact quasi-normal
modes than the P\"oschl-Teller potential, particularly for the first overtone.
We hope this work opens new perspectives to the computation of quasi-normal
modes and finds further improvements and generalizations in the future.
