On quasinormal frequencies of black hole perturbations with an external source

TL;DR

This paper investigates how external sources affect black hole quasinormal modes, showing that moderate sources do not alter existing frequencies but can introduce new modes, with implications for modified gravity theories.

Contribution

It demonstrates that external sources do not change quasinormal frequencies in rotating black holes and explores the emergence of new modes due to external driving forces.

Findings

Moderate sources do not modify existing quasinormal modes.

External sources can introduce new dissipative singularities and modes.

Numerical verification confirms analytical predictions.

Abstract

In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domain does not modify the quasinormal modes. Furthermore, we generalize our discussions to the case where the external source serves as a driving force. Different from an initial pulse, an external source may further drive the system to experience new perturbation modes. To be specific, novel dissipative singularities might be brought into existence and enrich the pole structure. This is a physically relevant scenario, due to its possible implication in modified gravity. Our arguments are based on exploring the pole structure of the solution in the Laplace s-domain with the presence of the external source. The analytical analyses are verified numerically by solving the inhomogeneous differential equation and extracting the dominant complex frequencies by employing the Prony method.