Quasinormal behavior of massless scalar field perturbation in Reissner-Nordstrom anti-de Sitter spacetimes

TL;DR

This work analyzes massless scalar perturbations of RNAdS black holes by computing quasinormal modes using both the Horowitz-Hubeny frequency-domain method and time-domain evolution. It identifies two stable families of modes, oscillatory and nonoscillatory, and maps how their frequencies depend on charge, overtone, and angular index, including a transition to a power-law tail in the extreme limit. The results confirm and refine previous findings, showing ω_I tends to zero at extremality while the decay remains finite via power-law tails, implying stability of extreme RNAdS to scalar perturbations. The study further characterizes high-overtone spectra and reveals a nontrivial quadratic dependence on ℓ, providing a richer picture of AdS BH perturbations relevant to holography and BH stability analyses.

Abstract

We present a comprehensive study of the massless scalar field perturbation in the Reissner-Nordstrom anti-de Sitter (RNAdS) spacetime and compute its quasinormal modes (QNM). For the lowest lying mode, we confirm and extend the dependence of the QNM frequencies on the black hole charge got in previous works. In near extreme limit, under the scalar perturbation we find that the imaginary part of the frequency tends to zero, which is consistent with the previous conjecture based on electromagnetic and axial gravitational perturbations. For the extreme value of the charge, the asymptotic field decay is dominated by a power-law tail, which shows that the extreme black hole can still be stable to scalar perturbations. We also study the higher overtones for the RNAdS black hole and find large variations of QNM frequencies with the overtone number and black hole charge. The nontrivial dependence of frequencies on the angular index is also discussed.

Figures (14)

• Figure 1: Illustration of the filtering process. (top) Data obtained from the characteristic algorithm. (bottom) The $\chi^{2}$-fitting made in the characteristic data subtracted from the Horowitz-Hubeny NOM solution. The results obtained from this fitting are compatible with the Horowitz-Hubeny OM results. In the graphs $r_{+}=100$, $Q/Q_{max} = 0.41$, $R=1$, $\ell=0$ and $n=0$.
• Figure 2: Semilog graphs of the scalar field in the event horizon, showing the transition from oscillatory to nonoscillatory asymptotic decay. In the graphs, $r_{+}=100$, $\ell=0$ and $R=1$.
• Figure 3: Graph of $\omega_{R}(OM)$ with $Q/Q_{max}$, using Horowitz-Hubeny method and characteristic integration results. For this graph, $r_{+}=100$, $R=1$, $\ell=0$ and $n=0$.
• Figure 4: Graph of $\omega_{I}$ (OM and NOM) with $Q/Q_{max}$, showing that $\omega_{I}(NOM)$ tends to zero as $Q$ tends to $Q_{max}$. In the graph, $r_{+}=100$, $R=1$, $\ell=0$ and $n=0$.
• Figure 5: Log-log graphs of the scalar field in the event horizon. (left) Extreme case for different values of $\ell$, showing power-law tails. If $\ell = 0$, $\Psi \propto v^{-2}$, but if $\ell > 0$, $\Psi \propto v^{-1}$. (right) Approach to the extreme limit, showing transition from exponential decay to power-law decay ($\ell=1$). For all curves, $r_{+}=100$ and $R=1$.