Proca field perturbations in higher-dimensional AdS and Schwarzschild-AdS spacetimes

David Duarte Cesar Lopes

Informações chave

Autores:

David Duarte Cesar Lopes (David Duarte Cesar Lopes)

Orientadores:

José Pizarro de Sande e Lemos (José Pizarro de Sande e Lemos)

Publicado em

11/12/2023

Resumo

Field perturbations in black hole spacetimes have been considered in a variety of contexts, from probing the dynamics of astrophysical black holes to studying quantum gravity theories. A perturbed spacetime vibrates with characteristic frequencies, known as quasinormal modes. In asymptotically anti-de Sitter (AdS) spacetimes, these are studied in the context of the AdS/conformal field theory (CFT) correspondence, where the quasinormal mode frequencies determine the thermalization timescale of the CFT. We study Proca field perturbations in d-dimensional AdS and Schwarzschild-AdS spacetimes. We obtain the Proca equations by decomposing the field according to its tensorial behaviour on the sphere. We demonstrate that the equations form two completely separated sectors: the vector-type sector, which accounts for d-3 decoupled degrees of freedom of the field, governed by a single wave-like equation; the scalar-type sector, which describes the remaining two degrees of freedom of the field, ruled by two coupled wave-like equations. We show that the latter decouple in higher-dimensional AdS, and we compute the exact normal mode solutions of Proca field perturbations in this spacetime, imposing Dirichlet boundary conditions at infinity. Additionally, the Maxwell field results are recovered by taking the massless limit of the Proca field. In Schwarzschild-AdS, linear stability is proved against vector-type and monopole Proca field perturbations. We also compute numerically the Proca field quasinormal modes in 4,5,6,7-dimensional Schwarzschild-AdS, and perform an analytical study of the spectrum for small black holes.