ON A SUFFICIENT CONDITION FOR THE METRIC COEFFICIENTS TO BE CONFORMALLY TIME-INDEPENDENT

The statement in Rindler's book "Essential Relativity" (Springer-Verlag, New York, 1977), p. 119 claiming that "the metric coefficients are time-independent if light signals tracing out the same path always take the same coordinate time" has two problems, the first one has been pointed out by us in a recent paper "relation between choosing ‘good' coordinates and the behavior of light signals" Acta Physica Sinica (Overseas Edition), 3(1994), 881, while the second is the main focus of the present article.