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Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F11%3A00064682" target="_blank" >RIV/00216224:14310/11:00064682 - isvavai.cz</a>

  • Result on the web

    <a href="http://iopscience.iop.org/0264-9381/28/14/145010/" target="_blank" >http://iopscience.iop.org/0264-9381/28/14/145010/</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1088/0264-9381/28/14/145010" target="_blank" >10.1088/0264-9381/28/14/145010</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions

  • Original language description

    Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg?Sachs theorem tofive dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weakerassumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/LC505" target="_blank" >LC505: Eduard Čech Center for Algebra and Geometry</a><br>

  • Continuities

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

Others

  • Publication year

    2011

  • 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

  • Volume of the periodical

    28

  • Issue of the periodical within the volume

    14

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    32

  • Pages from-to

    145010

  • UT code for WoS article

    000291789300010

  • EID of the result in the Scopus database