Complex scaling approach to quasinormal modes of Schwarzschild and Reissner--Nordström black holes
Shoya Ogawa, Takuya Hirose, Okuto Morikawa
TLDR
This paper uses the complex scaling method to unify the computation of black-hole quasinormal mode frequencies for Schwarzschild and Reissner--Nordström black holes.
Key contributions
- Applies the Complex Scaling Method (CSM) to black-hole perturbation equations.
- Converts the quasinormal mode problem into a non-Hermitian eigenvalue problem.
- Benchmarked CSM for the Schwarzschild Regge--Wheeler equation.
- Extended CSM to Reissner--Nordström black holes, including the extremal limit.
Why it matters
This paper introduces a unified and flexible approach, the Complex Scaling Method (CSM), for calculating black-hole quasinormal mode frequencies. It simplifies the complex outgoing-wave boundary condition into a standard eigenvalue problem. This method offers a robust framework for future studies of black hole perturbations and gravitational wave astronomy.
Original Abstract
We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge--Wheeler equation and then extend it to the Reissner--Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.
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