Figure 1

Quasinormal modes as a function of $a$ obtained by the Frobenius method for $D=7$, $l=2$, $j=0$: $m=4$ (blue line), $m=3$ (red line), $m=2$ (yellow line), $m=1$ (green line), $m=0$ (light blue line). Higher values of $m$ correspond to the larger real part of $\omega$.Reuse & Permissions

Figure 2

Quasinormal modes obtained by the Frobenius method for $D=7$, $l=2$, $j=0$: $m=-1$ (blue line), $m=-2$, $m=-3$, $m=-4$, $m=-5$ (light blue line), $m=-10$ (green line), $m=-15$ (red line), $m=-20$ (magenta line), $m=-25$ (brown line). Higher negative values of $m$ correspond to the larger real and imaginary part of $\omega$. The imaginary part of the QN frequency stays negative, implying stability against perturbations with the high negative azimuthal number $m$.Reuse & Permissions

Figure 3

Maximum value of the imaginary part of the quasinormal mode for negative values of $m$ together with the found fit $\max (\mathrm{Im}(\omega )\propto (-m{)}^{-\alpha }(\alpha >0)$ for $D=7$, $l=2$, $j=0$ (left figure, log-log scale) and corresponding values of the rotation parameter $a_{\max }$ as a function of $-m$ (right figure).Reuse & Permissions

Figure 4

Quasinormal modes obtained by the Frobenius method for $D=10$, $l=2$, $j=0$: $m=5$ (blue line), $m=4$ (red line), $m=3$ (yellow line), $m=2$ (green line), $m=1$ (light blue line). Higher values of $l$ correspond to the larger real part of $\omega$.Reuse & Permissions

Figure 5

Quasinormal modes obtained by the Frobenius method for $D=7$: ($l=2$, $m=0$, $j=0$—black line), ($l=2$, $m=0$, $j=1$—yellow line), ($l=2$, $m=0$, $j=2$—orange line), ($l=2$, $m=1$, $j=0$—purple line), ($l=2$, $m=1$, $j=1$—blue line), ($l=2$, $m=1$, $j=2$—magenta line), ($l=3$, $m=1$, $j=0$—green line), ($l=4$, $m=1$, $j=0$—cyan line), ($l=5$, $m=1$, $j=0$—red line). The larger values of $j$ correspond to the smaller values of the imaginary part of $\omega$. The real part increases with $l+m+2j$ for small rotation. When $a$ is large, the real part for the multipole index $j\ne 0$ approaches zero, while that for $j=0$ approaches $a$ constant that increases with $l$.Reuse & Permissions

Figure 6

Dependence of quasinormal modes obtained by the WKB method on the azimuthal number $m$ for $D=7$, $l=2$, $j=0$, $a=10$.Reuse & Permissions

Figure 7

Quasinormal modes as a function of $a$ for $D=8$, $l=2$, $m=0$, 1: $j=0$ (red line), $j=1$ (green line), $j=2$ (blue line). Higher $m$ and $j$ have larger real and imaginary parts of $\omega$.Reuse & Permissions

Figure 8

Quasinormal modes as a function of $a$ for $D=9$, $l=2$, $m=0$, 1: $j=0$ (red line), $j=1$ (green line), $j=2$ (blue line). Higher $m$ and $j$ have larger real and imaginary parts of $\omega$.Reuse & Permissions

Figure 9

Quasinormal modes as a function of $a$ for $D=11$, $l=2$, $m=0,1$: $j=0$ (red line), $j=1$ (green line), $j=2$ (blue line). Higher $m$ and $j$ have larger real and imaginary parts of $\omega$.Reuse & Permissions

Figure 10

Dependence of the quasinormal modes on $j$ for $D=8$ (blue line) and $D=9$ (red line), $a=7$, $m=1$. The plots with larger absolute values of $\mathrm{Re}(\omega )$ and $\mathrm{Im}(\omega )$ correspond to the larger $D$Reuse & Permissions