Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime

Abstract

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.

Dirac quasinormal modes of D-dimensional de Sitter spacetime

“…In Refs. [17], [23] we showed that the de Sitter QN frequencies are well defined for electromagnetic and gravitational perturbations in D ≥ 4 dimensions. Furthermore, in Ref.…”

“…Owing to its simplicity the propagation of classical fields in this spacetime has been studied, see for example [15]- [18], [21]- [27] and references therein. Its QNMs are defined as the solutions to the equations of motion for the classical fields that satisfy the boundary conditions [17], [22], [23]: (i) the field is regular at r = 0; (ii) the field is purely outgoing near the cosmological horizon.…”

“…In three and four dimensions these frequencies were already calculated in Refs. [16], [23]. Nevertheless, in the previous references for a Dirac field moving in D-dimensional de Sitter background, for D ≥ 5, the de Sitter QN frequencies were not computed.…”

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions

“…For the CAO black hole (37), if we propose a separable solution as that of the formula (6), then we obtain that the Klein-Gordon equation (5) simplifies to the radial differential equation…”

“…Nevertheless for some spacetimes their QNF are computed exactly and it should be noted that many of these gravitational systems are lower dimensional. In three dimensions we know the BTZ black hole [24]- [28], the warped AdS(3) black hole [29]- [31], the dilatonic black hole [32]- [35], and the de Sitter spacetime [36,37].…”