Abstract
We numerically calculate the quasinormal frequencies of the Klein-Gordon and Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory. For the Klein-Gordon field we use the Horowitz-Hubeny method and the asymptotic iteration method for second order differential equations. For the Dirac field we first exploit the Horowitz-Hubeny method. As a second method, instead of using the asymptotic iteration method for second order differential equations, we propose to take as a basis its formulation for coupled systems of first order differential equations. For the two fields we find that the results that produce the two numerical methods are consistent. Furthermore for both fields we obtain that their quasinormal modes are stable and we compare their quasinormal frequencies to analyze whether their spectra are isospectral. Finally we discuss the main results.
Highlights
The quasinormal modes (QNMs) are the oscillations of perturbed black holes that are purely ingoing near the horizon
In what follows we describe our numerical results for the quasinormal frequencies (QNFs) of the Klein–Gordon field and of the Dirac field
For the Dirac field propagating in the 2D black hole (2) we find that, for the first ten modes, the two methods produce QNFs that agree to three decimal places
Summary
The quasinormal modes (QNMs) are the oscillations of perturbed black holes that are purely ingoing near the horizon. The boundary condition imposed at the asymptotic region depends on its structure, for example, for asymptotically flat black holes the boundary condition usually imposed is that the perturbation is purely outgoing as r → ∞, whereas for the asymptotic anti-de Sitter black holes (asymptotically adS black holes, in what follows), a common boundary condition demands that the perturbation goes to zero as r → ∞ (Avis et al, 1978; Kokkotas and Schmidt, 1999; Berti et al, 2009; Konoplya and Zhidenko, 2011). It is well known that the QNFs of black holes are determined by the geometry and the type of perturbation (Kokkotas and Schmidt, 1999; Berti et al, 2009; Konoplya and Zhidenko, 2011)
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