What are the equations from which all of GR can be derived? Obviously one of the equations is Einstein's Field Equation: [itex]G^{\alpha\beta}=8\pi T^{\alpha\beta}[/itex]. I would also guess that you would need the Euler-Lagrange Equations: [itex]-\frac{d}{d\sigma}(\frac{\partial L}{\partial (dx^{\alpha}/d\sigma)}) + \frac{\partial L}{\partial x^{\alpha}} = 0[/itex]. Are those all the necessary equations, ie, if given a set initial conditions could you correctly calculate the entire history of the system using only these two equations and a lot of math (assuming of course that gravity is the only force)?(adsbygoogle = window.adsbygoogle || []).push({});

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# Mathematical Axioms of General Relativity

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