Higher dimensional bivectors and classification of the Weyl operator

被引：25

作者：

Coley, Alan ^{[1
]}

Hervik, Sigbjorn ^{[2
]}

机构：

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

[2] Univ Stavanger, Fac Sci & Technol, N-4036 Stavanger, Norway

来源：

CLASSICAL AND QUANTUM GRAVITY | 2010年 / 27卷 / 01期

关键词：

BLACK-HOLES; PETROV TYPE; SPACETIMES; IDENTITIES;

D O I：

10.1088/0264-9381/27/1/015002

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise to a refinement in dimensions higher than four of the usual alignment (boost-weight) classification, in terms of the irreducible representations of the spins. We are consequently able to define a number of new algebraically special cases. In particular, the classification in five dimensions is discussed in some detail. In addition, utilizing the (refined) algebraic classification, we are able to prove some interesting results when the Weyl tensor has (additional) symmetries.

引用

页数：21