English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Canonical energy is a valuable tool for analyzing the linear stability ofblack hole spacetimes; positivity of canonical energy for all perturbationsimplies mode stability, whereas the failure of positivity for any perturbationimplies instability. Nevertheless, even in the case of $4$-dimensionalSchwarzschild spacetime --- which is known to be stable --- manifest positivityof the canonical energy is difficult to establish, due to the presence ofconstraints on the initial data as well as the gauge dependence of thecanonical energy integrand. Consideration of perturbations generated by a Hertzpotential would appear to be a promising way to improve this situation, sincethe constraints and gauge dependence are eliminated when the canonical energyis expressed in terms of the Hertz potential. We prove that the canonicalenergy of a metric perturbation of Schwarzschild that is generated by a Hertzpotential is positive. We relate the energy quantity arising in the linearstability proof of Dafermos, Holzegel and Rodnianski (DHR) to the canonicalenergy of an associated metric perturbation generated by a Hertz potential. Wealso relate the Regge-Wheeler variable of DHR to the ordinary Regge-Wheeler andtwist potential variables of the associated perturbation. Since the Hertzpotential formalism can be generalized to a Kerr black hole, our results may beuseful for the analysis of the linear stability of Kerr.

Canonical Energy and Hertz Potentials for Perturbations of Schwarzschild Spacetime