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

Table 4

Reissner-Nordström quasinormal frequency parameter values (𝜌=−𝑖𝜔) for the fundamental (𝑛=0) and two lowest overtones for 𝑙=2 and 𝑖=2.

𝑛	𝑄	𝜌Leaver	𝜌AIM	𝜌WKB
0	0	(0.7473, −0.1779)	(0.7473, −0.1779) (<0.01%)(<0.01%)	(0.7463, −0.1784) (−0.13%)(−0.28%)
0	0.2	(0.7569, −0.1788)	(0.7569, −0.1788) (<0.01%)(<0.01%)	(0.7558, −0.1793) (−0.15%)(−0.28%)
0	0.4	(0.8024, −0.1793)	(0.8024, −0.1793) (<0.01%)(<0.01%)	(0.8011, −0.1797) (−0.16%)(−0.22%)
0	0.495	(0.8586, −0.1685)	(0.8586, −0.1685) (<0.01%)(<0.01%)	(0.8566, −0.1706) (−0.23%)(−1.25%)
1	0	(0.6934, −0.5478)	(0.6934, −0.5478) (<0.01%)(<0.01%)	(0.6920, −0.5478) (−0.20%)(−0.37%)
1	0.2	(0.7035, −0.5503)	(0.7035, −0.5502) (<0.01%)(0.02%)	(0.7020, −0.5522) (−0.21%)(−0.36%)
1	0.4	(0.7538, −0.5499)	(0.7538, −0.5499) (<0.01%)(<0.01%)	(0.7510, −0.5525) (−0.37%)(−0.47%)
1	0.495	(0.8070, −0.5140)	(0.8067, −0.5164) (−0.04%)(0.47%)	(0.8068, −0.5287) (0.01%)(−2.21%)
2	0	(0.6021, −0.9566)	(0.6021, −0.9566) (<0.01%)(<0.01%)	(0.6059, −0.9421) (0.63%)(1.52%)
2	0.2	(0.6129, −0.9599)	(0.6128, −0.9599) (0.02%)(<0.01%)	(0.6164, −0.9458) (0.57%)(1.47%)
2	0.4	(0.6703, −0.9531)	(0.6703, −0.9531) (<0.01%)(<0.01%)	(0.6717, −0.9455) (0.21%)(0.80%)
2	0.495	(0.7078, −0.8872)	(0.8350, −0.8347) (17.97%)(5.92%)	(0.7344, −0.9135) (2.66%)(−2.96%)