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

Table 13

Selected spin two eigenvalues, ₂𝐴_𝑙𝑚, obtained from the AIM for a Kerr black hole with varying values of 𝑐=𝑎𝜔 and 𝑚=1: the same number of iterations in the AIM, 𝑛_𝐴, and the number of recursions in the CFM, 𝑛_𝐶, for 𝑐=0.1,0.8 at a working precision of 15 digit precision, where results are presented to 10 s.f.

𝑙	𝑐=0.1; (𝑛𝐴 =𝑛𝐶 = 15,)	𝑐=0.8; (𝑛𝐴 = 35, 𝑛𝐶 = 70)	𝑐=−10𝑖; (𝑛𝐴 = 80, 𝑛𝐶 = 130 CFM)	𝑐=10; (𝑛A = 75, 𝑛𝐶 = 145)
2	−0.1391483511	−1.462479552	(12.44128209, 0.8956143162)	−101.8949078
3	5.929826236	5.247141863	(32.31138608, 1.302608040)	−63.74900642
4	13.95640426	13.45636668	(51.27922784, 1.946041848)	−30.35607486
5	23.96944247	23.54163307	(69.25750923, 3.012877154)	−4.557015739
6	35.97681567	35.58524928	(85.86796852, 4.990079008)	−2.555206382
7	9.98139515	49.61077286	(99.20081385, 6.801617108)	12.32203552