## Abstract

The Newman-Penrose formalism for obtaining the recent conserved quantities in general relativity is discussed and a group-theoretic interpretation is given to it. This is done by relating each triad of the orthonormal vectors on the sphere to an orthogonal matrix g. As a result, the spin-weighted quantities η become functions on the group of three-dimensional rotation, η = η(g), where g ∈ O_{3},. An explicit form for the matrix g is given and a prescription for rewriting η(g) as functions of the spherical coordinates is also given. We show that a quantity of spin weight s can be expanded as a series in the matrix elements T_{3m}^{j} of the irreducible representation of O_{3}, where s is fixed. Infinite- and finite-dimensional representations of the group SU_{2} are then realized in the spaces of η's and T_{3m}^{j}. It is shown that the infinitedimensional representation is not irreducible; its decomposition into irreducible parts leads to the expansion of η in the T_{3m} ^{j}, the latter providing invariant subspaces in which irreducible representations act.

Original language | English |
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Pages (from-to) | 569-574 |

Number of pages | 6 |

Journal | Journal of Mathematical Physics |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jan 1969 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics