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On a classification of conformal Killing tensors

О классификации конформных тензоров Киллинга

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

A natural classification scheme for the family of conformal Killing tensorsKa1…ap is introduced. It is based on the geometric properties of the fieldKa1a2…apta2…tap, wheret a is the tangent vector to an affinely parametrized geodesic. Elements of the various classes are shown to generate Killing tensors of the given metric, through well-defined procedures. Specific examples taken from general relativity are also examined in detail.

Riassunto

Si introduce uno schema naturale di classificazione per la classe dei tensori di Killing conformiKa1…ap, basato sulle proprietà geometriche del campoKa1a2…apta p, dovet a è il vettore tangente ad una geodetica parametrizzata in modo affine. Si dimostra che i campi appartenenti alle diverse classi generano, attraverso opportuni procedimenti, tensori di Killing per la metrica assegnata. Sono inoltre studiati in dettaglio esempi tratti dalla relatività generale.

Резюме

Предлагается естественная схема классификации для семейства конформных тензоров КиллингаKa1…ap. Схема классификации основана на геометрических свойствах поляKa1a2…aptap, гдеt a есть касательный вектор к аффинно параметризованной геодезической. Показывается, что элементы разлиных классов образуют тензоры Киллинга данной метрики. Подробно исследуются специальные примеры, взятые из общей теории отноьительности.

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Authors and Affiliations

  1. Istituto Matematico dell'Università, Via L. B. Alberti 4, 16132, Genova, Italia

    G. Caviglia & C. Zordan

  2. Istituto di Fisica Teorica dell'Università, Via U. Bassi 6, 27100, Pavia, Italia

    F. Salmistraro

  3. Sezione di Pavia, Istituto Nazionale di Fisica Nucleare, Italia

    F. Salmistraro

Authors
  1. G. Caviglia
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  2. C. Zordan
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  3. F. Salmistraro
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Additional information

Work done under the auspices of National Group for Mathematical Physics of C.N.R.

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Caviglia, G., Zordan, C. & Salmistraro, F. On a classification of conformal Killing tensors. Nuovo Cimento B 75, 161–170 (1983). https://doi.org/10.1007/BF02831170

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  • DOI: https://doi.org/10.1007/BF02831170

PACS. 02.40

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