We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in $D$-dimensional de Sitter spacetime ($D \geq 4$). We also study the quasinormal modes of a real massive scalar field and we compare our results with those of other references.Comment: 26 pages, 1 table. Some changes made according to referee's suggestions. Matches published version in GR

Using the monodromy method we calculate the asymptotic quasinormal (QN) frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter (SadS) black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter (AdS) spacetime.

We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape invariant. The method used to find the solutions works with the two Schrodinger equations of the partner potentials. Furthermore we study some of the properties of these potentials.

We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s = 1 2 , 1, 2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.

Some properties of the Hawking radiation emitted by the family of black holes of the Einstein-Maxwell-Dilaton with cosmological constant theory in three dimensions found by Chan and Mann are studied using the complex paths method and the Damour-Ruffini method. The exact values of the quasinormal frequencies of the massless Dirac field propagating on a particular black hole of this family are calculated. Taking as a basis the results obtained for the values of the quasinormal frequencies the instability of some modes is discussed. The extension of these results to the black holes of the Einstein-Maxwell-Dilaton theory in four dimensions is studied in the appendix.