How did Enstein fall into the Riemann trap?

Cauchy Curvature Tensor in the 3D geometric space is expressed as follows:

Fxx Fxy Fxz

Fyx Fyy Fyz

Fzx Fzy Fzz . . (1)

The equivalence of this tensor in the 4-dimensional unit is,

Fxx Fxy Fxz Fxt

Fyx Fyy Fyz Fyt

Fzx Fzy Fzz Fzt

Ftx  Fty Ftz   Ftt . . . (2)

We can express the forces tensor by the Laplacian formula,

∇2xx ∇2xy ∇2xz ∇2xt [U]

∇2yx ∇2yy ∇2yz ∇2yt [U]

∇2zx ∇2zy ∇2zz ∇2zt [U]

∇2tx ∇2ty  ∇2tz  ∇2tt [U] . . . (3)

Where t is time in the 4-dimensional unit space xyzt.

and Fxy= ∇^2yx U(x,y,z,t),Ftx =   ∇^2yt U(x,y,z,t). ., etc.

This tensor is called the Cairo  tensor to distinguish it from the steady-state Riemann tensor.

Note that:

i-Equation 3 when multiplied by the curvature tensor is by itself the general relativity in one phrase.

ii- Formula 2 reduces to Cauchy Formula 1 as dU/dt)partial approaches zero.

iii- The time-dependent Riemann tensor R relates the space-time curvature to the energy density U in a strange way,

Curvature C is equal or proportional to energy density (C=const1 .E . . . 4).

This is false and misleading relation since the correct relation should be Curvature is inversely proportional to U ( .U x C =Const 2 . . . 5) in accordance with the universal law of 4D Lorentz transformation law which implies that the unitary xyzt space is constant or conserved durind its motion.

But here comes the satanic trap where Einstein fell in without retun by following or trying to prove the wrong relation 4 instead of the correct one 5 .

The author assumes that Einstein did not understand physics to the extent he assumes the relation between space curvature and  energy density is a relation of proportionality where as space curvature should be inversely proportional to the energy density as implied by the 4D xyzt Lorentz universal law of physics:

The  spacetime is constant or conserved under motion.

However, Einstein went to his black magic recalled some thinking experiment we call black magic and erroneously proved his false rule in 1915 curvature induces energy density not the other way around.

The question arises: If Einstein procedure is wrong how it comes that his results are perfect

The answer is simple, both equations 4,5 can yield the same results if the square of the curvature tensor is I which is the second part of the satanic trap.

You are discussing Riemannian geometry and its completeness without even acknowledging the Hopf-Rinow theorem which addresses exactly these issues?