Covariant classification of conformal Killing vectors of locally conformally flat n-manifolds with an application to Kerr-de Sitter spacetimes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456418" target="_blank" >RIV/00216208:11320/22:10456418 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I5JnEO9r_j" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I5JnEO9r_j</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevD.106.084045" target="_blank" >10.1103/PhysRevD.106.084045</a>

Result language
angličtina
Original language name
Covariant classification of conformal Killing vectors of locally conformally flat n-manifolds with an application to Kerr-de Sitter spacetimes
Original language description
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat n-metric gamma of signature (r, s) modulo conformal transformations of gamma. This is done in terms of endomorphisms in the pseudo-orthogonal Lie algebra o(r + 1, s + 1) up to conjugation of the group O(r + 1, s + 1). The explicit classification is worked out in full for the Riemannian gamma case (r = 0, s = n). As an application of this result, we prove that the set of five-dimensional, (? > 0)-vacuum, algebraically special metrics with nondegenerate optical matrix, analyzed in [G. Bernardi de Freitas et al., Commun. Math. Phys. 340, 291 (2015).] is in one-to-one correspondence with the metrics in the Kerr- de Sitter-like class. This class [M. Mars et al., Classical Quantum Gravity 34, 095010 (2017).; M. Mars and C. Peon-Nieto, Phys. Rev. D 105, 044027 (2022).] exists in all dimensions, and its defining properties involve only properties at I. The equivalence between two seemingly unrelated classes of metrics points towards interesting connections between the algebraically special type of the bulk spacetime and the conformal geometry at null infinity.
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
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OECD FORD branch
10300 - Physical sciences

Project
<a href="/en/project/GA22-14791S" target="_blank" >GA22-14791S: Black hole spacetimes in a general dimension, their properties and interpretation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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