In article , "Phillip Helbig (undress to
reply)" writes:

Since the acceleration in a circular orbit is sqrt(GM/r^2), we get

v^4 = GMa_0.

In other words, the circular velocity is (in the low-acceleration
regime) independent of the radius, leading to the famous flat rotation
curves of spiral galaxies.

Mond introduces a new constant with the dimensions of acceleration, but
spiral galaxies don't have a constant ACCELERATION in the
low-acceleration regime, but rather a constant CIRCULAR VELOCITY.

If I pretend that our formulation of GR is incorrect in some manner not yet=
discovered, and that the constant circular velocities observed in galaxies=
, that are independent of R, are caused by spacetime curvature rather than =
a MOND change of Newtonian expectations, how must spacetime curvature be ch=
anging with radius?

Seems to me the circular velocity is constant, but, the radius of curvature=
is getting larger. So it seems like the spacetime curvature would be gett=
ing smaller. But that it would not be getting smaller by as fast as we wou=
ld normally expect using current GR formulation.

Just trying to understand how we would understand the observation **IF** it=
were due to spacetime curvature. Would spacetime curvature be falling off=
by 1/R or some other factor?

Ross