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

Table 8

The QNM frequencies for the Scalar Perturbations of the Kerr Black Hole, with 𝑎=0.80 (𝑀=1, 𝑚=0). Numerical data via the CFM 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	0.1145–0.0957i	0.1005–0.1007i	0.1211–0.0897i	0.1141–0.0939i
			(−12.2%, 5.22%)	(5.76%, −6.23%)	(−0.35%, −1.88%)
1	0	0.3067–0.0901i	0.3029–0.0891i	0.3053–0.0893i	0.3052–0.0892i
			(−1.24%, −1.11%)	(−0.46%, −0.89%)	(−0.49%, −1.00%)
	1	0.2820–0.2783i	0.2758–0.2779i	0.2821–0.2755i	0.2817–0.2756i
			(−2.20%, −0.14%)	(0.04%, −1.01%)	(−0.11%, −0.97%)
2	0	0.5071–0.0897i	0.5035–0.0885i	0.5041–0.0886i	0.5041–0.0886i
			(−0.71%, −1.34%)	(−0.59%, −1.23%)	(−0.59%, −1.23%)
	1	0.4906–0.2722i	0.4866–0.2693i	0.4885–0.2690i	0.4885–0.2689i
			(−0.82%, −1.07%)	(−0.43%, −1.18%)	(−0.43%, −1.21%)
	2	0.4609–0.4634i	0.4585–0.4570i	0.4607–0.4581i	0.4606–0.4579i
			(−0.52%, −1.38%)	(−0.04%, −1.14%)	(−0.06%, −1.19%)