Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00508337" target="_blank" >RIV/67985840:_____/19:00508337 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1088/1361-6382/ab329a" target="_blank" >http://dx.doi.org/10.1088/1361-6382/ab329a</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6382/ab329a" target="_blank" >10.1088/1361-6382/ab329a</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation

Popis výsledku v původním jazyce

In linearized gravity, two linearized metrics are considered gauge-equivalent, , when they differ by the image of the Killing operator, . A universal (or complete) compatibility operator for K is a differential operator K 1 such that and any other operator annihilating K must factor through K 1. The components of K 1 can be interpreted as a complete (or generating) set of local gauge-invariant observables in linearized gravity. By appealing to known results in the formal theory of overdetermined PDEs and basic notions from homological algebra, we solve the problem of constructing the Killing compatibility operator K 1 on an arbitrary background geometry, as well as of extending it to a full compatibility complex K i (), meaning that for each K i the operator K i+1 is its universal compatibility operator. Our solution is practical enough that we apply it explicitly in two examples, giving the first construction of full compatibility complexes for the Killing operator on these geometries. The first example consists of the cosmological FLRW spacetimes, in any dimension. The second consists of a generalization of the Schwarzschild–Tangherlini black hole spacetimes, also in any dimension. The generalization allows an arbitrary cosmological constant and the replacement of spherical symmetry by planar or pseudo-spherical symmetry.

Název v anglickém jazyce

Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation

Popis výsledku anglicky

In linearized gravity, two linearized metrics are considered gauge-equivalent, , when they differ by the image of the Killing operator, . A universal (or complete) compatibility operator for K is a differential operator K 1 such that and any other operator annihilating K must factor through K 1. The components of K 1 can be interpreted as a complete (or generating) set of local gauge-invariant observables in linearized gravity. By appealing to known results in the formal theory of overdetermined PDEs and basic notions from homological algebra, we solve the problem of constructing the Killing compatibility operator K 1 on an arbitrary background geometry, as well as of extending it to a full compatibility complex K i (), meaning that for each K i the operator K i+1 is its universal compatibility operator. Our solution is practical enough that we apply it explicitly in two examples, giving the first construction of full compatibility complexes for the Killing operator on these geometries. The first example consists of the cosmological FLRW spacetimes, in any dimension. The second consists of a generalization of the Schwarzschild–Tangherlini black hole spacetimes, also in any dimension. The generalization allows an arbitrary cosmological constant and the replacement of spherical symmetry by planar or pseudo-spherical symmetry.

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

2019

Kód důvěrnosti údajů

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

Název periodika

Classical and Quantum Gravity

ISSN

0264-9381

e-ISSN

—

Svazek periodika

36

Číslo periodika v rámci svazku

18

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

40

Strana od-do

185012

Kód UT WoS článku

000482601900005

EID výsledku v databázi Scopus

2-s2.0-85073079064