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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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