Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00554419" target="_blank" >RIV/67985840:_____/22:00554419 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3842/SIGMA.2022.011" target="_blank" >https://doi.org/10.3842/SIGMA.2022.011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3842/SIGMA.2022.011" target="_blank" >10.3842/SIGMA.2022.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations

Popis výsledku v původním jazyce

We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a complete separation of variables, the radial mode equations form complicated systems of coupled linear ODEs. We outline a precise abstract strategy to decouple these systems into sparse triangular form, where the diagonal blocks consist of spin-s scalar Regge-Wheeler equations (for spins s=0,1,2). Building on the example of the vector wave equation, which we have treated previously, we complete a successful implementation of our strategy for the Lichnerowicz wave equation. Our results go a step further than previous more ad-hoc attempts in the literature by presenting a full and maximally simplified final triangular form. These results have important applications to the quantum field theory of and the classical stability analysis of electromagnetic and gravitational perturbations of the Schwarzschild black hole in harmonic gauges.

Název v anglickém jazyce

Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations

Popis výsledku anglicky

We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a complete separation of variables, the radial mode equations form complicated systems of coupled linear ODEs. We outline a precise abstract strategy to decouple these systems into sparse triangular form, where the diagonal blocks consist of spin-s scalar Regge-Wheeler equations (for spins s=0,1,2). Building on the example of the vector wave equation, which we have treated previously, we complete a successful implementation of our strategy for the Lichnerowicz wave equation. Our results go a step further than previous more ad-hoc attempts in the literature by presenting a full and maximally simplified final triangular form. These results have important applications to the quantum field theory of and the classical stability analysis of electromagnetic and gravitational perturbations of the Schwarzschild black hole in harmonic gauges.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-07776S" target="_blank" >GA18-07776S: Vyšší struktury v algebře, geometrii a matematické fyzice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

—

Svazek periodika

18

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

57

Strana od-do

011

Kód UT WoS článku

000752363700001

EID výsledku v databázi Scopus

2-s2.0-85124747941