The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F20%3AA0000066" target="_blank" >RIV/47813059:19610/20:A0000066 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10231-019-00924-y" target="_blank" >https://link.springer.com/article/10.1007/s10231-019-00924-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-019-00924-y" target="_blank" >10.1007/s10231-019-00924-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors

Popis výsledku v původním jazyce

We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the two-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order scalar differential invariants suitable for solution of the equivalence problem. Genericity means that the Killing leaves are not null, the metric is not orthogonally transitive (i.e., the distribution orthogonal to the Killing leaves is non-integrable), and two explicitly constructed scalar invariants C rho and lC are nonzero. All the invariants are designed to have tractable coordinate expressions. Assuming the existence of two functionally independent invariants, we solve the equivalence problem in two ways. As an example, we invariantly characterize the Van den Bergh metric. To understand the non-generic cases, we also find all Lambda-vacuum metrics that are generic in the above sense, except that either C rho or lC is zero. In this way we extend the Kundu class to Lambda-vacuum metrics. The results of the paper can be exploited for invariant characterization of classes of metrics and for extension of the set of known solutions of the Einstein equations.

Název v anglickém jazyce

The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors

Popis výsledku anglicky

We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the two-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order scalar differential invariants suitable for solution of the equivalence problem. Genericity means that the Killing leaves are not null, the metric is not orthogonally transitive (i.e., the distribution orthogonal to the Killing leaves is non-integrable), and two explicitly constructed scalar invariants C rho and lC are nonzero. All the invariants are designed to have tractable coordinate expressions. Assuming the existence of two functionally independent invariants, we solve the equivalence problem in two ways. As an example, we invariantly characterize the Van den Bergh metric. To understand the non-generic cases, we also find all Lambda-vacuum metrics that are generic in the above sense, except that either C rho or lC is zero. In this way we extend the Kundu class to Lambda-vacuum metrics. The results of the paper can be exploited for invariant characterization of classes of metrics and for extension of the set of known solutions of the Einstein equations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

1618-1891

Svazek periodika

199

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

38

Strana od-do

1343-1380

Kód UT WoS článku

000494394800001

EID výsledku v databázi Scopus

2-s2.0-85074749914