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Of course gravity is ubiquitous because classical level gravity is the curvature in the four-dimensional (4D)  spacetime continuum.
Gravity is not a force in the way electromagnetism is. Pure gravity motion of sourceless test particles is along the force-free straightest path "geodesics" in curved 4D spacetime. The curvature is from very massive bodies or even from the self-interaction of gravity as in Wheeler's geons and in primordial black holes (pure vacuum solutions with the source tensor Tuv(matter) = 0).
In contrast, the electromagnetic force pushes charged test particles off these straightest geodesic paths.
Yes, you can certainly try to think in terms of gravity vacuum current densities. That is one way of looking at Einstein's Guv tensor.
Simply replace "T" below by "G" and "mass" by "GeoMetroDynamic (GMD) field" in

G00 = local density of the GMD field.
G0i = GMD field flux across the xi surface is equivalent to the density of the ith component of GMD field's linear momentum
The problem with all this, however, is that locally Guv = 0 in the vacuum.
Guv = Ruv - (1/2)Rguv
each term on the RHS is separately zero in a classical vacuum.
However, when the quantum zero point fluctuations are retained we do get
Guv ~ /guv =/= 0
/ > 0 is dark energy de Sitter (dS) anti-gravity repulsive stretching of spacetime above and beyond the cosmological expansion of the Hubble flow.
/ < 0 is dark matter anti de Sitter (AdS) gravity attractive compression of spacetime etc.
What / is locally is scale-dependent.
virtual bosons make / > 0
virtual fermion-antifermion closed loops make / < 0
the two compete against each other
the / term is usually too small to detect.
if we can amplify it we have warp drive wormhole time travel super-technology.
Identifying the components of the tensor (Wiki)
In the following i and k range from 1 through 3.
The time-time component T00 ss the density of relativistic mass, i.e. the energy density divided by the speed of light squared,
The flux of relativistic mass across the xi surface T0i is equivalent to the density of the ith component of linear momentum,
The components Tij
represent flux of i momentum across the xk surface. In particular,

(not summed) represents normal stress which is called pressure when it is independent of direction. Whereas
represents shear stress (compare with the stress tensor).
Warning: In solid state physics and fluid mechanics, the stress tensor is defined to be the spatial components of the stress-energy tensor in the comoving frame of reference. In other words, the stress energy tensor in engineering differs from the stress energy tensor here by a momentum convective term.
On Nov 18, 2010, at 11:32 AM, JACK SARFATTI wrote:
On Nov 18, 2010, at 11:06 AM, This email address is being protected from spambots. You need JavaScript enabled to view it. wrote:
 Isaac Newton thought his falling Apple was pulled to the ground, that modern science speaks of attracting interactive forces between the Apple and the earths center of gravity, a pull force."
Yes, that's historically correct Roy, but that was more than three hundred years ago. We now know better. Einstein's theory has replaced Newton's.
Newton's equations and Einstein's are very similar under ordinary conditions we encounter, however the conceptual picture is very different. Paul Zielinski and Jonathan Post tried to explain this difference to you. I suggest you carefully read
Your mind needs to make a quantum leap to Einstein's way of thinking. You are stuck in Newton's way of thinking. You are inside a smaller box very hard to break out of even for some physicists and especially for engineers because Newton's force picture works very well practically speaking - but it is an illusion.
2010 10:29:00 P.M. Pacific Standard Time
From:    This email address is being protected from spambots. You need JavaScript enabled to view it.   writes;
“Matter tells Spacetime how to curve, and Spacetime tells matter how to move.”  
"I interpret this as reflecting the conjecture that Spacetime is not
simply a mathematically convenient tool for calculating and graphing
the effects of relativity; but that it also is the actual physical
mechanism by which gravity operates. That is, gravity actually changes
the physical geometry of local space and time."
This explanation is close enough for me Jack. If this is true, gravity is ubiquitous. If it tells matter how to move then it is some kind of force infinitely long, smooth and uniform. A metaphor for this would be similar to a flowing current (a constant) curving around a small rock and pushing it along a river bottom. The same (universal equivalent) current would exert different curvature pressures (space-time equivalent) differently against bigger rocks. You see Jack equations describe something. Universe is not made of equations they simply help us understand to profit from and build upon what God has created.