# Rigorous derivation of general relativity from first principles

1. What is the minimal set of axioms required to derive the mathematical formulation of General Relativity from first principles? What are these first principles?

2. How does such a derivation go step by step? (starting from something very abstract and adding axioms after axioms to finally lead to the Einstein equations?)

• I think that if you put the rather harsh requirement of not having higher than second order derivatives, you can narrow down the models to just GR. – G. Paily Jun 1 '16 at 0:43
• @G.Paily I don't think that rules out Einstein-Cartan or Brans-Dicke. (The latter is only ruled out by experiment IIRC.) – Ryan Unger Jun 1 '16 at 0:45
• @ocelo7 hmm, I'll grant you Brans-Dicke, but since the OP talked about using a set of axioms, surely we could just add a zero torsion axiom to rule out Eintein-Cartan? – G. Paily Jun 1 '16 at 0:49
• @G.Paily: Einstein guessed right, then wrong, then right again on the cosmological constant. Removing antisymmetric components, i.e. favoring Einstein over Einstein-Cartan is completely irrational because with them the cosmological singularity problem disappears. Brans-Dicke is, as far as I know, still not ruled out and then there are things like Scalar-Vector-Tensor gravity which can't be ruled out per observation, yet, but has the necessary degrees of freedom to fit things like rotation curves and mass profiles of galaxy clusters. And with seven parameters one can fit an elephant. – CuriousOne Jun 1 '16 at 0:51
• I can't link because it is a book, but MTW (Gravitation) lists 6 different routes to the Einstein Field Equations. – m4r35n357 Jun 1 '16 at 8:14