We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations.We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN) and Kerr black holes in a unified way. An advantage of the AIM over the standard continued fraction method (CFM) is that for differential equations with more than three regular singular points Gaussian eliminations are not required. However, the convergence of the AIM depends on the location of the radial or angular position, choosing the best such position in general remains an open problem. This review presents for the first time the spin 0, 1/2 & 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM, and confirms results previously obtained using the CFM.We also presents some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher dimensional generalizations and we give an example of doubly rotating black holes.

In previous works we have studied spin-3/2 fields near 4-dimensional Schwarzschild black holes.The techniques we developed in that case have now been extended here to show that it is possible to determine the potential of spin-3/2 fields near D-dimensional black holes by exploiting the radial symmetry of the system. This removes the need to use the Newman-Penrose formalism, which is difficult to extend to D-dimensional space-times. In this paper we will derive a general Ddimensional gauge invariant effective potential for spin-3/2 fields near black hole systems. We then use this potential to determine the quasi-normal modes and absorption probabilities of spin-3/2 fields near a D-dimensional Schwarzschild black hole.

In this work we calculate the angular eigenvalues of the (n + 4)-dimensional simply rotating Kerr-(A)dS spheroidal harmonics using the Asymptotic Iteration Method (AIM). We make some comparisons between this method and that of the Continued Fraction Method (CFM) and use the latter to check our results. We also present analytic expressions for the small rotation limit up to O(c 3 ) with the coefficient of each power up to O(α 2 ), where c = aω and α = a 2 Λ (a is the angular velocity, ω the frequency and Λ the cosmological constant). 1 Unlike the asymptotically flat limit (Λ = 0) which only has three regular singular points. 2 Of course some manipulation is first required to put the equation into the AIM form.

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The propagation of classical gravitational waves in Bianchi type-I universes is studied. We find that gravitational waves in Bianchi type-I universes are not equivalent to two minimally coupled massless scalar fields as in the Robertson-Walker universe. Because of its tensorial nature, the gravitational wave is much more sensitive to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe. PACS numberts): 04.30. Nk, 95.30.Sf, 98.80.H~