On the Goldberg?Sachs theorem in higher dimensions in the non-twisting case
Result description
We study a generalization of the shearfree part? of the Goldberg?Sachs theorem for Einstein spacetimes admitting a non-twisting multiple Weyl aligned null direction (WAND) in n>5 spacetime dimensions. The form of the corresponding optical matrix ? is restricted by the algebraically special property in terms of the degeneracy of its eigenvalues. In particular, there necessarily exists at least one multiple eigenvalue, and further constraints arise in various special cases. For example, when ? is non-degenerate and certain (boost weight zero) Weyl components do not vanish, all eigenvalues of ? coincide and such spacetimes thus correspond to the Robinson?Trautman class. On the other hand, in certain degenerate cases all non-zero eigenvalues can be distinct. We also present explicit examples of Einstein spacetimes admitting some of the permitted forms of ?, including examples violating the optical constraint?.
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The result's identifiers
Result code in IS VaVaI
Result on the web
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Alternative languages
Result language
angličtina
Original language name
On the Goldberg?Sachs theorem in higher dimensions in the non-twisting case
Original language description
We study a generalization of the shearfree part? of the Goldberg?Sachs theorem for Einstein spacetimes admitting a non-twisting multiple Weyl aligned null direction (WAND) in n>5 spacetime dimensions. The form of the corresponding optical matrix ? is restricted by the algebraically special property in terms of the degeneracy of its eigenvalues. In particular, there necessarily exists at least one multiple eigenvalue, and further constraints arise in various special cases. For example, when ? is non-degenerate and certain (boost weight zero) Weyl components do not vanish, all eigenvalues of ? coincide and such spacetimes thus correspond to the Robinson?Trautman class. On the other hand, in certain degenerate cases all non-zero eigenvalues can be distinct. We also present explicit examples of Einstein spacetimes admitting some of the permitted forms of ?, including examples violating the optical constraint?.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Classical and Quantum Gravity
ISSN
0264-9381
e-ISSN
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Volume of the periodical
30
Issue of the periodical within the volume
7
Country of publishing house
GB - UNITED KINGDOM
Number of pages
38
Pages from-to
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UT code for WoS article
000316227500016
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2013