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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/LC505" target="_blank" >LC505: Centrum Eduarda Čecha pro algebru a geometrii</a><br>

Návaznosti

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

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Classical and Quantum Gravity

ISSN

0264-9381

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

14

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

32

Strana od-do

145010

Kód UT WoS článku

000291789300010

EID výsledku v databázi Scopus

—