Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime

TL;DR

This paper systematically derives the linearized dynamics of massive and partially massless spin-2 fields around (anti) de Sitter black holes, analyzing mode spectra, isospectrality, and symmetry properties across dimensions.

Contribution

It provides a comprehensive derivation of the quadratic actions and equations of motion for these fields in various dimensions, including new analytical results on isospectrality.

Findings

Analytical proof of isospectrality for L=1 modes in 4D de Sitter.

Demonstration that isospectrality breaks in higher dimensions.

Explicit symmetry form underlying isospectrality in 4D.

Abstract

We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schr\"odinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number $L=1$ in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.