Off-shell duality invariance of Schwarzschild perturbation theory

TL;DR

This paper investigates the duality invariance in Schwarzschild perturbation theory, revealing conserved quantities and showing that even- and odd-parity perturbations share equal Love numbers, with derivations of related action principles and identities.

Contribution

It demonstrates off-shell duality invariance in Schwarzschild perturbations and derives new action principles and identities related to these symmetries.

Findings

Even- and odd-parity perturbations have equal Love numbers.

Derived an action principle for the Fackerell-Ipser equation.

Established off-shell duality invariance leading to conserved quantities.

Abstract

We explore the duality invariance of the Maxwell and linearized Einstein-Hilbert actions on a non-rotating black hole background. On shell these symmetries are electric-magnetic duality and Chandrasekhar duality, respectively. Off shell they lead to conserved quantities; we demonstrate that one of the consequences of these conservation laws is that even- and odd-parity metric perturbations have equal Love numbers. Along the way we derive an action principle for the Fackerell-Ipser equation and Teukolsky-Starobinsky identities in electromagnetism.