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

Table 2

QNMs to 6 signifcant figures for Schwarzschild de Sitter gravitational perturbations (𝑠=2) for ℓ=2 and ℓ=3 modes. We only present results for the AIM method, because the results are identical to those of the CFM after a given number of iterations (in this case 50 iterations for both methods). The 𝑛=1,2 modes can be compared with the results in [30] for 𝑠=2.

Λ(ℓ=2)	𝑛=1	𝑛=2	𝑛=3
0	0.373672–0.0889623i	0.346711–0.273915i	0.301050–0.478281i
0.02	0.338391–0.0817564i	0.318759–0.249197i	0.282732–0.429484i
0.04	0.298895–0.0732967i	0.285841–0.221724i	0.259992–0.377092i
0.06	0.253289–0.0630425i	0.245742–0.189791i	0.230076–0.319157i
0.08	0.197482–0.0498773i	0.194115–0.149787i	0.187120–0.250257i
0.09	0.162610–0.0413665i	0.160789–0.124152i	0.157042–0.207117i
0.10	0.117916–0.0302105i	0.117243–0.0906409i	0.115876–0.151102i
0.11	0.0372699–0.00961565i	0.0372493–0.0288470i	0.0372081–0.0480784i
Λ(ℓ=3)	𝑛=1	𝑛=2	𝑛=3
0	0.599443–0.0927030i	0.582644–0.281298i	0.551685–0.479093i
0.02	0.543115–0.0844957i	0.530744–0.255363i	0.507015–0.432059i
0.04	0.480058–0.0751464i	0.471658–0.226395i	0.455011–0.380773i
0.06	0.407175–0.0641396i	0.402171–0.192807i	0.392053–0.322769i
0.08	0.317805–0.0503821i	0.315495–0.151249i	0.310803–0.252450i
0.09	0.261843–0.0416439i	0.260572–0.124969i	0.257998–0.208412i
0.10	0.189994–0.0303145i	0.189517–0.0909507i	0.188555–0.151609i
0.11	0.0600915–0.00961888i	0.0600766–0.0288567i	0.0600469–0.0480945i