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On theories of gravitation in which the dynamical equations do not follow from the field equations and the Birkhoff Theorem
Author(s) -
Bleyer U.,
Mücket J. P.
Publication year - 1980
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2103010604
Subject(s) - generalization , gravitation , physics , field equation , dynamical systems theory , classical mechanics , classical field theory , tetrad , gravitational field , field (mathematics) , theoretical physics , mathematical physics , mathematics , mathematical analysis , quantum mechanics , pure mathematics
In general the Birkhoff theorem is violated in non‐Einsteinian theories of gravitation. We show for theories in which the dynamical equations do not follow from the field equations that time‐dependent vacuum solutions are needed in order to join nonstatic spherically symmetric incoherent matter distributions. It is shown for Treder's tretrad theories that such vacuum solutions exist and a continuous and unique junction is possible. In generalization of these results we consider the problem in what theories of gravitation the dynamical equations do not follow from the field equations. This consideration leads to non‐Einsteinian theories like bimetric theories or Treder's tetrad theories containing supplementary geometrical quantities which are not dynamical variables of the theory.