Normal modes of Proca fields in AdS spacetime

TL;DR

This paper analytically determines the normal modes and frequencies of Proca fields in AdS spacetime, demonstrating the decoupling of equations via vector spherical harmonics and recovering Maxwell fields in the massless limit.

Contribution

It provides an analytical method to find normal modes of Proca fields in AdS spacetime by decoupling equations through VSH basis change, including the Maxwell limit.

Findings

Normal modes and frequencies are analytically derived.

Equations for Proca fields can be decoupled analytically.

Maxwell fields are recovered in the massless limit.

Abstract

A normal mode analysis for Proca fields in the anti-de Sitter (AdS) spacetime is given. It is found that the equations for the Proca field can be decoupled analytically. This is performed by changing the basis of the vector spherical harmonics (VSH) decomposition. The normal modes and the normal mode frequencies of the Proca equation in the AdS spacetime are then analytically determined. It is also shown that the Maxwell field can be recovered by taking the massless limit of the Proca field with care so that the nonphysical gauge modes are eliminated.