General relativity and conformal invariance

In this, the first of a pair of related papers, it is argued that general relativity allows more freedom in the choice of the metric than is usually supposed. In particular, conformally equivalent classes of metrics are to be regarded as physically equivalent. The theory is thus conformally invariant -a fact which is obscured by the non-conformally covariant way in which the field equations are usually written. Furthermore, there may be situations in which this usual way of writing the field equations is liable to give misleading results in the same way that a bad choice of co-ordinate system can lead to non-physical results. Another representation is given which does not suffer from this disadvantage. (author)