Normal modes of Proca fields in AdS${}_d$ spacetime

Abstract

The normal modes of Proca field perturbations in $d$-dimensional anti-de Sitter spacetime, AdS${}_d$ for short, with reflective Dirichlet boundary conditions, are obtained exactly. Within the Ishibashi-Kodama framework, we decompose the Proca field in scalar-type and vector-type components, according to their tensorial behavior on the $(d-2)$-sphere ${\mathcal{S}}^{d-2}$. Two of the degrees of freedom of the Proca field are described by scalar-type components, which in general are coupled due to the mass of the field, but in AdS${}_d$ we show that they can be decoupled. The other $d-3$ degrees of freedom of the field are described by a vector-type component that generically decouples completely. The normal modes and their frequencies for both the scalar-type and vector-type components of the Proca field are then obtained analytically. Additionally, we analyze the normal modes of the Maxwell field as the massless limit of the Proca field. We find that for scalar-type perturbations in $d=4$ there is a discontinuity in the massless limit, in $d=5$ the massless limit is well defined using Dirichlet-Neumann rather than Dirichlet boundary conditions, and in $d>5$ the massless limit is completely well defined, i.e., it is obtained smoothly from the massless limit of the scalar-type perturbations of the Proca field. For vector-type perturbations the Maxwell field limit is obtained smoothly for all $d$ from the massless limit of the vector-type perturbations of the Proca field.

arXiv comment16 pages

References in corpus (16)

• On weakly turbulent instability of anti-de Sitter space
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter spacetimes: A complete study on the asymptotic behavior
• Massive vector fields on the Schwarzschild spacetime: quasinormal modes and bound states
• Static response and Love numbers of Schwarzschild black holes
• Scalar Collapse in AdS
• Massive vector field perturbations in the Schwarzschild background: stability and quasinormal spectrum
• Perturbations and Stability of Static Black Holes in Higher Dimensions
• Electromagnetic quasinormal modes of D-dimensional black holes
• Hawking radiation for a Proca field in D-dimensions
• Quasinormal modes of Proca fields in a Schwarzschild-AdS spacetime
• Maxwell perturbations on asymptotically anti-de Sitter spacetimes: Generic boundary conditions and a new branch of quasinormal modes
• Massive vector field perturbations on extremal and near-extremal static black holes
• New islands of stability with double-trace deformations
• Normal modes of Proca fields in AdS spacetime