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

Table 3

Comparison of the first few QNMs to 6 significant figures for Schwarzschild anti-de-Sitter scalar perturbations (𝑠=0) for ℓ=0 modes with 𝑟₊=1. The second column corresponds to data [40] using the Horowitz and Hubeny (HH) method [38], while the third column is for the AIM using 70 iterations. [*] Note the mismatch for the real part of the 𝑛=3 mode in [40]; we have confirmed this using the Mathematica notebook provided in [24].

𝑛	HH method	AIM
0	2.7982–2.6712i	2.79823–2.67121i
1	4.75849–5.03757i	4.75850–5.03757i
2	6.71927–7.39449i	6.71931–7.39450i
3	8.68223[*]–9.74852i	8.68233–9.74854i
4	10.6467–12.1012i	10.6469–12.1013i
5	12.6121–14.4533i	12.6125–14.4533i
6	14.5782–16.8049i	14.5788–16.8050i
7	16.5449–19.1562i	16.5457–19.1563i