The following is a question regarding the derivation of Einstein's field equations.(adsbygoogle = window.adsbygoogle || []).push({});

Background

In deriving his equations, it is my understanding that Einstein equated theEinstein Tensor Gand the_{μv}Cosmological Constant*Metric Tensorwith theStress Energy Momentum Tensor Tterm simply because the covariant derivative of all three terms equals zero._{μv}

R_{μv}- (1/2)*g_{μv}*R + [itex]\Lambda[/itex]*g_{μv}= (8*pi*G)/(c^{4})*T_{μv}

Question

Is this basis for equivalence (that terms are equivalent if their covariant derivatives are equal) standard practice in mathematics, or did Einstein take a leap of faith?

Thank you very much for your time! Please let me know if I can clarify my question.

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# Einstein's Basis for Equivalence in his Field Equations

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