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

Table 9

The QNM frequencies for the spin half 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 [48], where the AIM was set to run at 15 iterations.

𝑙	𝑛	Numerical	Third-order WKB	Sixth-order WKB	AIM
0	0	0.1830–0.0970i	0.1765–0.1001i (−3.55%, 3.20%)	0.1827–0.0949i (−0.16%, −2.16%)	0.1830–0.0969i (<0.01%, −0.10%)
1	0	0.3800–0.0964i	0.3786–0.0965i (−0.37%, 0.10%)	0.3801–0.0964i (0.03%, <0.01%)	0.3800–0.0964i (<0.01%, <0.01%)
	1	0.3558–0.2975i	0.3536–0.2987i (−0.62%, 0.40%)	0.3559–0.2973i (0.03%, −0.07%)	0.3568–0.2976i (0.28%, 0.03%)
2	0	0.5741–0.0963i	0.5737–0.0963i (−0.07%,<0.01%)	0.5741–0.0963i (<0.01%, <0.01%)	0.5741–0.0963i (<0.01%, <0.01%)
	1	0.5570–0.2927i	0.5562–0.2930i (−0.14%, 0.10%)	0.5570–0.2927i (<0.01%, <0.01%)	0.5573–0.2928i (0.05%, 0.03%)
	2	0.5266–0.4997i	0.5273–0.4972i (0.13%, −0.50%)	0.5265–0.4997i (−0.02%, <0.01%)	0.5189–0.5213i (−1.46%, 4.32%)