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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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, (? &gt; 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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, (? &gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GA22-14791S" target="_blank" >GA22-14791S: Černoděrové prostoročasy v obecné dimenzi, jejich vlastnosti a interpretace</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Physical Review D

ISSN

2470-0010

e-ISSN

2470-0029

Svazek periodika

106

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

084045

Kód UT WoS článku

000878751300004

EID výsledku v databázi Scopus

2-s2.0-85141562259