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

Table 10

The QNM frequencies for the spin half perturbations of the Kerr black hole, with 𝑎=0.80 (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(J)	Sixth-order WKB(J)	AIM
0	0	0.1932–0.0891i	0.1883–0.0896i (−2.54%, 0.56%)	0.1914 –0.0865i (−0.93%, −2.92%)	0.1920–0.0872i (−0.62%, −2.13%)
1	0	0.3993–0.0893i	0.3956–0.0881i (−0.93%, −1.34%)	0.3967–0.0880i (−0.65%, −1.46%)	0.3965–0.0880i (−0.70%, −1.46%)
	1	0.3789–0.2728i	0.3751–0.2701i (−1.00%, −0.99%)	0.3777–0.2687i (−0.32%, −1.50%)	0.3764 – 0.2517i (−0.66%, −7.73%)
2	0		0.5984–0.0881i	0.5987–0.0881i	0.5987–0.0882i (<0.01%, 0.11%)
	1		0.5844–0.2669i	0.5855–0.2667i	0.5846–0.2644i (−0.15%, −0.86%)
	2		0.5600–0.4512i	0.5609–0.4517i	0.6023–0.4260i (7.38%, −5.70%)