Loop tests during scalar invariant
generation are omitted.
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,
the scalar invariant for Kepler's 3rd Law for the simple point-mass, as originally obtained by Karl Schwarzschild  for his particular solution.
which is a scalar invariant for the photon orbit about the point-mass.
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.
is a scalar invariant which shows that the angular velocity approaches a finite limit, in contrast to Newton's theory where it becomes unbounded.
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.
It obtains the finite limit given in (23), which is a scalar invariant for the point-charge.
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