The field equation proposed by Penney and Marathe, the interesting mathematical properties of which have been studied by Marathe, is discussed from an original physical point of view. In particular, this equation is shown to admit solutions which are qualitatively different from analogous solutions of the Einstein equation since they have no singularity.

It has been observed by Marathe that the Einstein equation is equivalent to a system of two equations, one of which is the conservation equation. The other one has very interesting mathematical properties and has been proposed as field equation for a gravitational theory more general than Einstein's.

One may object that this theory does not involve conservation of energy. However, it is well known that, in general, the equation $T^{ij}{}_{;j}=0$, which arises from the Einstein equation, cannot be interpreted as global conservation of energy: in order to perform this interpretation, we need nonzero Killing vector fields, which do not exist on a generic space-time. What we have, in general, is only local  conservation of energy. On the other hand, there is no experimental evidence that energy is conserved on a large scale; this means that there is no a priori  reason to discard a field equation such that $T^{ij}{}_{;j}\neq0$, provided that it reduces approximately to the Einstein equation on a small scale.

For this reason, Marathe's theory may have physical interest and is studied in this paper from a physical point of view.