Math of General Relativity - Part 19

If you want to look at the equation relating the matrix G with the mass, energy and motion (or Stress-Energy Tensor) of the gravitating matter, see the below link.

So now we know how to assign a Matrix of 16 numbers to each point P in space inside MSG at each point in time. On Earth, these numbers won't change with time, to a huge degree of accuracy. Now we want to translate this point P inside MSG to a point P4 on a Riemann surface in Riemann Space.

Relating a space-time point P (x ,y, z, t) in real space-time to the surface, or Riemann Space R4, can be done using the simple "mapping" equations x = u1, y = u2, z = u3 and u4 = ct, where c is the speed of light , and the U are the coordinate axes on the surface of R4.

This gives us a point P4 = (u1, u2, u3, u4) in R4, or on the surface R4, whichever way you want to look at it.

Theory: This point P4 was mapped from MSG to R4, and the value of the gravitational field G at the point P4 is the value of the Metric Tensor at P4.

In other words, the theory is that real space-time and gravity in real space-time can be translated into a purely GEOMETRIC mathematical scenario. Gravity in 3D space-time produces a 4D surface in an alternate 4D mathematical Universe. How this is not the "real" Universe will be shown next.

https://mathworld.wolfram.com/EinsteinFieldEquations.html