Il Nuovo Cimento (1955-1965)

, Volume 26, Issue 1, pp 53–62 | Cite as

On Cauchy’s problem in general relativity - II

  • A. Peres
Article

Summary

It is always possible to satisfy the three transverse constraints πmn.n= 0 by taking πmn=δS/δgmn, whereS is any functional of thegmn, invariant under co-ordinate transformations. If furthermore S is invariant under scale transformations, we also havegmnπmn = 0. The explicit construction of initial data for General Eelativity then reduces to the Lichnerowicz scalar equation, and can be achieved with arbitrary accuracy. This method can be considered as a first step towards a Hamilton-Jacobi formalism for the gravitational field.

Riassunto

È sempre possibile soddisfare le tre costrizioni trasversali πmn,n = π prendendo πmn= δS/δgmn, in cui8 è un qualsiasi funzionale delgmn, invariante per trasformazioni di coordinate. Se inoltreS è invariante per trasformazioni di scala, noi abbiamo anchegmnπmn = 0. La costruzione esplicita dei dati iniziali della relativita generale si riduce allora all’equazione scalare di Lichnerowicz. Questo metodo puo essere considerate un primo passo verso un formalismo di Hamilton-Jacobi per il campo gravitazionale.

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Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • A. Peres
    • 1
  1. 1.Palmer Physical LaboratoryPrinceton UniversityPrinceton
  2. 2.Israel Institute of TechnologyHaifa

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