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

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Publikace nespadá pod Pedagogickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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TAGHAVI-CHABERT Arman

Rok publikování 2011
Druh Článek v odborném periodiku
Časopis / Zdroj Classical and Quantum Gravity
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www http://iopscience.iop.org/0264-9381/28/14/145010/
Doi http://dx.doi.org/10.1088/0264-9381/28/14/145010
Obor Obecná matematika
Klíčová slova Robinson manifolds; algebraically special higher-dimensional spacetimes
Popis 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 to five 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 weaker assumptions 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.
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