The Palatini variational principle for the general Bergmann–Wagoner–Nordtvedt theory of gravitation

Abstract

The Hilbert variational principle for the Bergmann–Wagoner–Nordtvedt scalar–tensor theory of gravitation is presented in a general form, yielding the field equations in arbitrary units. Applying then the Palatini method of variation to this action integral, the connection can be shown to be an integrable Weyl connection, even if the matter part contains explicitly the connection coefficients. However, the resulting field equations always appear in the wrong unit system, or turn out to be wrong in a general gauge.