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

Table 11

Spin-2 angular separation constants and Kerr gravitational quasinormal frequencies for the fundamental mode corresponding to 𝑙=2 and 𝑚=0 compared with the CFM [6] (𝑀=1/2).

𝑎	𝐴Leaver	𝐴AIM	𝜔Leaver	𝜔AIM
0	(4.0000, 0.0000)	(4.0000, 0.0000) (<0.01%)(<0.01%)	(0.7473, −0.1779)	(0.7413, −0.1780) (−0.80%)(−0.06%)
0.1	(3.9972, 0.0014)	(3.9973, 0.0014) (<0.01%)(<0.01%)	(0.7502, −0.1774)	(0.7444, −0.1775) (−0.77%, −0.06%)
0.2	(3.9886, 0.0056)	(3.9887, 0.0056) (<0.01%)(<0.01%)	(0.7594, −0.1757)	(0.7540, −0.1763) (−0.71%)(−0.03%)
0.3	(3.9730, 0.0126)	(3.9733, 0.0126) (<0.01%)(<0.01%)	(0.7761, −0.1720)	(0.7715, −0.1722) (−0.59%)(−0.12%)
0.4	(3.9480, 0.0223)	(3.9482, 0.0222) (<0.01%)(−0.45%)	(0.8038, −0.1643)	(0.8025, −0.1639) (−0.16%)(0.24%)
0.45	(3.9304, 0.0276)	(3.9303, 0.0280) (<0.01%)(1.45%)	(0.8240, −0.1570)	(0.8250, −0.1591) (0.12%)(−1.34%)