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When we study basic General Relativity, the interior solution of Schwarzschild spacetime sometimes are skipped. In order to determine the $\kappa = \displaystyle \frac{8\pi G}{c^{4}}$ constant of EFE we rewrite the EFE in terms of energy momentum tensor,i.e. (in components),

$$R_{ab} = \kappa \displaystyle \left(T_{ab}-\frac{1}{2}T^{c}_{c}g_{ab}\right).$$

But why we use this form to study the derivation of a stellar interior? (I mean the classical form of EFE: $$R_{ab} - \frac{1}{2}Rg_{ab} = \kappa T_{ab}.$$ Does not already "encoded" the final relation between energy distribuition and geometry?Classically,of course.)

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    $\begingroup$ Are you asking why the two forms are equivalent? They of course are, and a hint to what's going on in the common nickname for the Einstein tensor: "Trace reversed Ricci Tensor" (which, strictly speaking is only appropriate for four dimensions, which is the whole World in relativity though). Otherwise, the answer is that the form you quote is simply more convenient for certain calculations. $\endgroup$ – WetSavannaAnimal Mar 12 '18 at 3:05
  • $\begingroup$ @WetSavannaAnimalakaRodVance If you state in a comment that "the answer is ..." and explain your reasoning there's no sensible reason not be make a proper answer out of it, IMO. $\endgroup$ – StephenG Mar 12 '18 at 3:55
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    $\begingroup$ Possible duplicate of: physics.stackexchange.com/q/387428 $\endgroup$ – mmeent Mar 12 '18 at 10:56

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