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

Table 5

Reissner-Nordström quasinormal frequency parameter values (𝜌=−𝑖𝜔) for the fundamental (𝑛=1) and two lowest overtones for 𝑙=2 and 𝑖=1.

𝑛	𝑄	𝜌Leaver	𝜌AIM	𝜌WKB
0	0	(0.9152, −0.1900)	(0.9152, −0.1900) (<0.01%)(<0.01%)	(0.9143, −0.1901) (−0.10%)(−0.05%)
0	0.2	(0.9599, −0.1929)	(0.9599, −0.1929) (<0.01%)(<0.01%)	(0.9590, −0.1930) (−0.09%)(−0.05%)
0	0.4	(1.1403, −0.1984)	(1.1403, −0.1981) (<0.01%)(0.15%)	(1.1395, −0.1980) (−0.07%)(−0.20%)
0	0.495	(1.3855, −0.1773)	(1.3855, −0.1773) (<0.01%)(<0.01%)	(1.3850, −0.1783) (−0.04%) (−0.56%)
1	0	(0.8731, −0.5814)	(0.8731, −0.5814) (<0.01%)(<0.01%)	(0.8717, −0.5819) (−0.16%)(−0.09%)
1	0.2	(0.9200, −0.5894)	(0.9200, −0.5894) (<0.01%)(<0.01%)	(0.9186, −0.5897) (−0.15%)(−0.05%)
1	0.4	(1.1100, −0.6021)	(1.1100, −0.6021) (<0.01%)(<0.01%)	(1.1081, −0.6014) (−0.17%)(0.12%)
1	0.495	(1.3573, −0.5350)	(1.3573, −0.5350) (<0.01%)(<0.01%)	(1.3579, −0.5423) (0.04%)(−1.36%)
2	0	(0.8024, −1.0032)	(0.8024, −1.0032) (<0.01%)(<0.01%)	(0.8046, −0.9917) (0.27%)(1.15%)
2	0.2	(0.8530, −1.0143)	(0.8530, −1.0143) (<0.01%)(<0.01%)	(0.8548, −1.0037) (0.21%)(1.05%)
2	0.4	(1.0582, −1.0263)	(1.0582, −1.0263) (<0.01%)(<0.01%)	(1.0568, −1.0181) (−0.13%)(0.80%)
2	0.495	(1.3019, −0.9024)	(1.3019, −0.9024) (<0.01%)(<0.01%)	(1.3141, −0.9222) (0.94%)(−2.19%)