Il Nuovo Cimento (1955-1965)

, Volume 34, Issue 2, pp 317–339 | Cite as

A covariant multipole formalism for extended test bodies in general relativity

  • W. G. Dixon


A discussion and criticism is given of various forms that have been put forward for the multipole theory of an extended test body in curved space-time, and a new treatment is proposed, in which the effect of an electromagnetic field is included and in which the covariance is retained throughout by the use of bitensors. Included in this is a covariant definition of the world-line of the mass centre. Equations of motion are derived in the pole-dipole approximation and a comparison is made with the previous theories. It is seen that, although the new theory avoids the defects mentioned in the former theories, solutions of our equations satisfy those of the former theories if terms quadratic in the spin are neglected.


Si discutono e si criticano le varie forme, che sono state esposte sinora, della teoria multipolare di un corpo di prova esteso nello spazio-tempo curvo, e si propone un nuovo trattamento, in cui si tien conto dell’effetto di un campo elettromagnetico nel quale si mantiene dappertutto l’evidente covarianza con l’uso di bitensori. In questo si comprende una definiziore covariante della linea universale del centro di massa. si deducono le equazioni del moto nell’approssimazione polo-dipolo e si fa un confronto con le teorie precedenti. Si vede che, sebbene la nuova teoria eviti i difetti menzionati nelle precedenti teorie, le soluzioni delle nostre equazioni soddisfano quelle delle teorie precedenti se si trascurano termini quadratici nello spin.


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Copyright information

© Proprietà Letteraria Riservata 1964

Authors and Affiliations

  • W. G. Dixon
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridge

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