Superradiance and Quasinormal Modes of Massive Scalar Fields around Kerr Black Holes in Einstein-Maxwell-Dilaton-Axion Theory with Perfect Fluid Dark Matter

Abstract

We investigate the dynamics of massive scalar fields around Kerr black holes in the Einstein-Maxwell-Dilaton-Axion (EMDA) theory, incorporating the effects of perfect fluid dark matter (PFDM), characterized by the dilaton parameter $r_2$ and the PFDM parameter $λ$. These parameters modify both the ergosphere and the effective potential experienced by the scalar field. Using the asymptotic matching method, we compute superradiant amplification factors, while quasinormal mode (QNM) frequencies are obtained via the asymptotic iteration method (AIM). Our results reveal contrasting effects: increasing $r_2$ enhances superradiance and leads to higher QNM frequencies with greater damping, whereas increasing $λ$ suppresses superradiance and reduces QNM frequencies with weaker damping. In combined scenarios, the influence of $λ$ is found to be dominant. These findings extend the understanding of Kerr black holes in EMDA backgrounds and highlight the stabilizing role of PFDM in such systems.

Figures (11)

• Figure 1: Effect of $r_2$ (left) and $\lambda$ (right) on $\Delta_D(r)$ for a Kerr black hole with $M=1$ and $a=0.8$.
• Figure 2: Profiles of the Kerr–EMDA effective potential for a massive scalar field with real frequency. (a) Left panel: variation with the dilaton parameter $r_2$ at fixed PFDM parameter $\lambda = 0.15$. (b) Right panel: variation with $\lambda$ at fixed $r_2 = 0.16$. The black hole mass and spin are $M = 1$ and $a = 0.8$, with azimuthal mode $m = 1$, scalar mass $\mu = 0.1$, and real frequency $\omega = 0.08$. Changes in $r_2$ and $\lambda$ modify the location and height of the potential barrier, thereby influencing the superradiant scattering process.
• Figure 3: Profiles of the Kerr–EMDA effective potential for a massive scalar field with complex frequency, complementing the real-frequency case shown in Fig. \ref{['fig:PotentialPlotsRealOmega']}. Real, imaginary, and absolute values of the potential are plotted as functions of the tortoise coordinate $r_*$ for $\omega = 0.2 - 0.1 i$. (a) Left panels: variation with the dilaton parameter $r_2$ at fixed PFDM parameter $\lambda = 0.15$. (b) Right panels: variation with $\lambda$ at fixed $r_2 = 0.16$. Black dots indicate the local minima of the potential profiles. The parameters are $M = 1$, $a = 0.8$, $m = 1$, and $\mu = 0.1$. Variations in $r_2$ and $\lambda$ shift the potential minima and alter the barrier shape, affecting mode stability and amplification.
• Figure 4: Low-frequency amplification factor $|Z_{22}|$ computed from Eq. \ref{['Eq:Zlm-EMDA-PDFM']} as a function of frequency $\omega$ for a Kerr black hole ($r_2 = 0$, $\lambda = 0$) (left) and a black hole with dilaton charge $r_2 = 0.16$ and PFDM parameter $\lambda = 0.1$ (right), with spins $a = \{0.6, 0.7, 0.8, 0.9\}$. Parameters: $M = 1$, $\mu = 0.1$, $l = 2$, $m = 2$. Increasing spin enhances the superradiant amplification and broadens the corresponding frequency window.
• Figure 5: Same as Fig. \ref{['fig:ZlmSpin']}, but showing the dependence on the dilaton parameter $r_2$ and PFDM parameter $\lambda$. Left: $\lambda = 0.15$, $r_2 = \{0.0, 0.08, 0.16, 0.24, 0.32\}$. Right: $r_2 = 0.16$, $\lambda = \{0.0, 0.05, 0.10, 0.15\}$. Parameters: $M = 1$, $\mu = 0.1$, $l = 2$, $m = 2$, $a = 0.8$. Increasing the dilaton parameter $r_2$ enhances the superradiant amplification, whereas increasing the PFDM parameter $\lambda$ suppresses it.