A constant

scalar invariant (CSI) space-time is a space-time such that all of the polynomial

scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant.

* Loop tests during

scalar invariant generation are omitted.

According to (24), [square root of [C.sub.n](D([r.sub.0]))[equivalent to] [alpha]] is a scalar invariant, being independent of the value of [r.sub.0].

which is a scalar invariant. Thus, no curvature singularity can arise in the gravitational field of the simple point-charge.

is a scalar invariant; and for the simple point-charge is,

the scalar invariant of Kepler's 3rd Law for the simple point-charge; and when a = q = 0, (9) reduces to the near-field limit,

C([r.sub.0])=[[alpha].sup.2] emphasizes the true meaning of [alpha], viz., [alpha] is a scalar invariant which fixes the spacetime for the pointmass from an infinite number of mathematically possible forms, as pointed out by Abrams.

Equation (19) shows that =2[pi]a is also a scalar invariant for the point-mass.

The sought for complete solution for the point-mass must reduce to the general solution for the simple point-mass in a natural way, give rise to an infinite sequence of particular solutions in each particular configuration, and contain a scalar invariant which embodies all the factors that contribute to the effective gravitational mass of the field's source for the respective configurations.

Thus, f([r.sub.0]) is a scalar invariant for the point-charge.

[2] Dusek, Z.:

Scalar invariants on special spaces of equiaffine connections, J.

It has been proved elsewhere [3, 4] that in the case of the simple "point-mass" (a fictitious object), metrics of the form (8) or (9) are characterised by the following

scalar invariants,