"Gravity Force" outmoded concept

The analogy of gravity force with electrical force is not very good. However, take a large flat charged conducting plate.

http://www.math.uni-bremen.de/~justen/Forschung/ie_condenser.jpg

Near its center the electric force field is approximately uniform in analogy with a uniform gravity force field in Newton's picture. Above picture is for a condenser with oppositely charge plates that give similar effect. I am talking about the RED region.

That is there is a finite region of space in which approximately from Gauss's law

Grad^2V ~ source density

doing integrals and using symmetry

V(Coulomb) ~ Ez

z is normal distance to plate

the force per unit mass on a test particle charge q and mass m is

a = -(q/m)dV/dz = - (q/m)E

E ~ spatially uniform in limited region

In Newtonian gravity from potential theory there is a similar Gauss law

V(Newton) ~ gz

a = g

Approximately uniform

What this means in Einstein's theory is the following.

The approximate metric can be written as (c = 1)

ds^2 ~ -(1 - gz)dt^2 + (1 - gz)^-1dz^2 + dx^2 + dy^2

gz << 1

For the rest "shell" LNIF hovering observers

dz(LNIF shell) = dz/(1 - gz)^1/2 ~ dz(1 + gz/2)

dt(LNIF shell) = dt(1 - gz)^1/2 ~ dt(1 - gz/2)

The z distance between stationary nongeodesic shell observers is larger than the "book keeping" amount (if there were no source) by gz/2

Note the approximation gz << 1.

i.e. gz/c^2 << 1

The gravity red shift is for a receiver far away and sender at z is for frequency of signal f

f(receiver) ~ f(sender)(1 - gz/2c^2)

only from that limited region.

The important part of the connection field here is

c^2{^z00} ~ g

but that is only in the non-geodesic SHELL FRAME.

It's not frame-invariant.

Note in electricity

The electromagnetic force is a tensor

f^u = (q/m)F^uvV^v

But in gravity in Einstein's theory

the Newtonian "gravity force" is not a tensor

g ~ c^2{z,00}

The shell LNIF observers must provide a non-gravity force to keep at fixed z in the above problem

This is CONTINGENT - not INTRINSIC.

There is no intrinsic gravity force in Einstein's theory. All gravity force is 100% inertial depending on arbitrary choice of the non-geodesic needing a non-gravity force to exist. The curvature field is intrinsic i.e. a tensor, but it is geodesic deviation independent of arbitrary choices of non-geodesics from non-gravity forces. There is never any "g-force" on a massive test particle on a timelike geodesic in curved space-time. The test particle acceleration on a geodesic is zero. The intrinsic classical geometrodynamic field is fully determined by the geodesic structure. Intrinsic curvature is "geodesic deviation". All non-geodesics are contingent not necessary and they require external non-gravity forces to create. Null event horizons are barriers (one-way membranes) to all timelike worldlines whether geodesic or nongeodesic). Spacelike worldlines pass through event horizons but on-mass-shell tachyons usually signal a vacuum ODLRO instability and are not themselves stable. Post-quantum signal nonlocality observed in the CIA SRI experiments of Puthoff & Targ and confirmed in other experiments
http://www.signonsandiego.com/news/science/20060622-9999-lz1c22cause.html
do not change the above considerations. That is, non-light signal based nonlocal C^3 will not provide "absolute simultaneity". Classical GR geometrodynamics is not affected by post-quantum signal nonlocality that is a mental process confined to living conscious matter far from thermal equilibrium.
http://xxx.lanl.gov/abs/quant-ph/0203049