Today we use all the tools we've got in our back pocket to "derive" the Einstein Field Equations of general relativity. It's more of a motivation than a derivation, I suppose.

This series is based off the book "Tensor Calculus for Physics" by Dwight Neuenschwander:
https://amzn.to/3rEema3

Video relating metric to gravitational potential:
   • Relating Metric Tensor to Gravity | T...  

Video deriving contracted bianchi identity:
   • The Bianchi Identities | Tensor Calcu...  

Deriving the Riemann Curvature Tensor:
   • Tensor Calculus Ep. 15 | Riemann Curv...  

Uniqueness of Riemann Curvature Tensor:
https://vixra.org/pdf/1912.0357v1.pdf

or
https://physics.stackexchange.com/que...

0:00 Intro
1:40 Goal: Generalize Poissons Equation
4:40 Criteria for Field Equations
12:09 What Could They be in Terms of?
15:13 "Guessing" the Form of the EFE's
18:41 Finding the Coefficients
32:23 Writing Down Einsteins Equations
33:52 Important Interpretation
34:04 Conclusion