Petrov D vacuum spaces revisited: identities and invariant classification

被引：9

作者：

Edgar, S. Brian ^{[1
]}

Gomez-Lobo, Alfonso Garcia-Parrado ^{[1
]}

Martin-Garcia, Jose M. ^{[1
,2
,3
]}

机构：

[1] Linkoping Univ, Inst Matemat, SE-58183 Linkoping, Sweden

[2] Univ Paris Diderot, CNRS, Observ Paris, Lab Univers & Theories, F-92190 Meudon, France

[3] Univ Paris 06, CNRS, Inst Astrophys Paris, F-75014 Paris, France

来源：

CLASSICAL AND QUANTUM GRAVITY | 2009年 / 26卷 / 10期

关键词：

NULL GEODESIC SEPARABILITY; GENERAL-RELATIVITY; ORTHOGONAL TRANSITIVITY; KARLHEDE CLASSIFICATION; PERFORMING CALCULATIONS; COSMOLOGICAL CONSTANT; TETRAD FORMALISMS; PENROSE FORMALISM; FIELD-EQUATIONS; MAPLE PACKAGE;

D O I：

10.1088/0264-9381/26/10/105022

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for the four GHP derivatives on each of the four GHP spin coefficients and the one Weyl tensor component. It follows directly from these results that the theoretical upper bound on the order of covariant differentiation of the Riemann tensor required for a Karlhede classification of these spaces is reduced to two.

引用

页数：13