We first explain the fundamental rules governing the physics of the universe.

Physics stems only from the universal laws of nature.

They form the basis of mathematics, physics, chemistry, geometry, and all the sciences we know.

*Rule 1: The universal laws of physics are unprovable and cannot be deduced or proven.

Anyone who mistakenly attempts to prove one or more universal laws of physics is practicing black magic, not science.

Note that the great A. Einstein (who is still my idol) fell into this trap when he tried to derive the universal law of the Lorentz transformation in 1D and 3D, calling them special and general relativity, which is nothing more than low-grade black magic.

Now let's return to general relativity:

Rule 1*- We assert that the tensor forces per unit area F in a control volume of entangled particles, or energy density in xyzt space, correspond to its ∇2 U(x,y,z,t) at the required point.

For example, ∇2xx = Fxx, ∇2xy = Fxy, ∇2tx = Ftx.

It is clear that ∇2xy = d^2U/dx (dy)partial and ∇2xt (d^2U/dx (dt)partial, etc.) Therefore, the stress tensor is expressed as follows:

∇2xx ∇2xy ∇2xz ∇2xt [U(x,y,z,t)

∇2yx ∇2yy ∇2yz ∇2yt [U(x,y,z,t)

∇2zx ∇2zy ∇2zz ∇ zt [U(x,y,z,t)

∇2tx ∇2ty ∇ 2tz ∇2tt [U(x,y,z,t)

Matrix 1

Rule 2*- We also assert that the curvature of spacetime is Cij.

In other words, Cxy is the x-curvature of xy and Cyt is the y-curvature, etc.

Therefore, the curvature tensor of spacetime is given by:

Cxy Cxy Cxz Cxt

Cyx Cyy Cyz Cyt

Czx Czy Czz Czt

Ctx Cty Ctz Ctt

Matrix 2

Rule 3* We reaffirm that the little-known and rarely mentioned Lorentz transformation law in 4 dimensions is a universal law of physics and implies that the unit xyzt space is conserved for the system within the control volume under consideration.

In other words,

Matrix 1 * Matrix 2 = I . .(3)

Where I is the unit matrix.

X∇2xx ∇2xy ∇2xz ∇2xt [U(x,y,z,t)∇2yx ∇2yy ∇2yz ∇2yt [U(x,y,z,t)∇2zx ∇2zy ∇2zz ∇ zt [U(x,y,z,t)∇2tx ∇2ty ∇ 2tz ∇2tt [U(x,y,z,t)

Cxy Cxy Cxz Cxt

Cyx Cyy Cyz Cyt

Czx Czy Czz Czt

Ctx Cty Ctz Ctt . . .= I . . . (3)

Equation 3 itself constitutes the desired rigorous formula for general relativity in its new, modern form.

It should be noted that the theory of special relativity, which is the Lorentz transformation law in one dimension, is only a special case and can be deduced from Equation 3.