A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method

Table 7

The QNM frequencies for the Scalar Perturbations of the Kerr Black Hole, with 𝑎=0.00, that is, the Schwarzschild limit (𝑀=1, 𝑚=0). Numerical data via the CFM were taken from [45, 46], where the AIM was set to run at 15 iterations.

𝑙	𝑛	Numerical	Third-order WKB(J)	Sixth-order WKB(J)	AIM
0	0	0.1105–0.1049i	0.1046–0.1001i	0.1105–0.1008i	0.1103–0.1046i
			(−5.34%, 9.82%)	(<0.01%, −2.91%)	(−0.18%, –0.29%)
1	0	0.2929–0.0977i	0.2911–0.0989i	0.2929–0.0978i	0.2929–0.0977i
			(−0.61%, 1.23%)	(<0.01%, 0.10%)	(<0.01%, <0.01%)
	1	0.2645–0.3063i	0.2622–0.3074i	0.2645–0.3065i	0.2645–0.3063i
			(−0.87%, 0.36%)	(<0.01%, 0.07%)	(<0.01%, <0.01%)
2	0	0.4836–0.0968i	0.4832–0.0968i	0.4836–0.0968i	0.4836–0.0968i
			(−0.08%, <0.01%)	(<0.01%, <0.01%)	(<0.01%, <0.01%)
	1	0.4639–0.2956i	0.4632–0.2958i	0.4638–0.2956i	0.4639–0.2956i
			(−0.15%, 0.07%)	(−0.02%, <0.01%)	(<0.01%, <0.01%)
	2	0.4305–0.5086i	0.4317–0.5034i	0.4304–0.5087i	0.4306–0.5086i
			(0.28%, −1.02%)	(−0.02%, 0.02%)	(0.02%, <0.01%)