### Abstract

The properties of principal null directions of a perturbed black hole are investigated. It is shown that principal null directions are directly observable quantities characterizing the spacetime. A definition of a perturbed spacetime, generalizing that given by Stewart and Walker, is proposed. This more general framework allows one to include descriptions of a given spacetime other than by a pair (M, g) where M is a four-dimensional differential manifold and g a Lorentz metric. Examples of alternative characterizations are the curvature representation of Karlhede and others, the Newman-Penrose representation or observable quantities involving principal null directions. The conditions are studied under which the various alternative choices of observables provide equivalent descriptions of the spacetime.

Original language | English |
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Pages (from-to) | 5241-5252 |

Number of pages | 12 |

Journal | Classical and Quantum Gravity |

Volume | 20 |

Issue number | 24 |

DOIs | |

Publication status | Published - Dec 21 2003 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Classical and Quantum Gravity*,

*20*(24), 5241-5252. https://doi.org/10.1088/0264-9381/20/24/001