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

Understand

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.