...gravity

On these theories, see, e.g., Will (1993) and Damour & Esposito-Farèse (1992), and references therein.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...one

A clear distinction between the "Einstein" frame and the "Jordan" frame, may be found, e.g., in Damour & Nordverdt (1993)

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...by

We introduce a minus sign in (20) because Eqs.(12) and (14) imply that $a^{\mu}$ is a space-like vector when the electromagnetic field is not a pure gauge field.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...equations

These equations mean that $v^{\mu} = \alpha \eta^{\mu}$, where $\alpha=const.$ and $\eta^{\mu}$ is a connection vector of the system of light rays associated with the phase function S (see, e.g., Schneider et al. 1992).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...action

For details see Will (1993) and references therein. The factor $-(16 \pi c)^{-1}$ in the gravitational action is due to the fact that we use the definition of the energy-momentum tensor given in Landau & Lifshitz (1975).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...by

This transformation can be suggested by the conformal transformation of the metric which passes from the Jordan-Fierz frame to the Einstein frame.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.