In my paper in Phys. Letts..vol 68A (1978)409-411, I have discussed a metric

projectively related to Friedman/R-W metric with identical geodesics.Questions:

Are there other such solutions for this case or for other conformaly flat

spaces? One such solution defines an infinite succession. Is there a computer

program to find infinite succession of (covariant)Einstein tensors.; the

change represents the erruption of matter-energy in assumed spontaneous

projective change. on approach to a singularity. Physically the change is

caused by intervention of Gauge fields to avoid gravity-induced collapse.

The point is that addition to Christofell connection of a term (Identity tensor

times Vector) leaves a system of geodesics unchanged,and is in accord

with equivalence principle. This way one can relate both gauge field and

Q.M. with G .R..Details on request.See also Matsience Report no92(1978)/

paper 9,14pp (www.imsc.res.in/Library)-Black Body Structure of a Black

Hole. And  Lie Structure of Quasiconformal Maps in R*(*=N). And Physics of

String Theory in Quantum Field Theory. QM,& Optics- Ed VV Dodonov &

V I Manko , Moscow (1990) Nova Publishers (N,Y)vol 187 of Proc 0f Lebedev Phy. Inst.Acad. 0f Sciences 0f the USSR./pp113-116..