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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA18-07776S" target="_blank" >GA18-07776S: Higher structures in algebra, geometry and mathematical physics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Name of the periodical

Classical and Quantum Gravity

ISSN

0264-9381

e-ISSN

—

Volume of the periodical

36

Issue of the periodical within the volume

18

Country of publishing house

GB - UNITED KINGDOM

Number of pages

40

Pages from-to

185012

UT code for WoS article

000482601900005

EID of the result in the Scopus database

2-s2.0-85073079064