I have a Straightforward question. When the functional derivative of the Ricci scalar to get the GR field equations. As the derivative is done using the metric which is symmetric do I have to symmetrize my results.
On mathematica with the package xAct the "VarD" function always symmetrizes when I do a variation with a symmetric tensor.
For normal GR as I understand the symmetry pops out on its own, but as I'm working on other formulations of GR, sometimes this symmetry isn't a given.
Edit: As pointed in the comments by Qmechanic there is a similar answered question: Variation of the metric with respect to the metric I'm convinced now, as I expected, that I should symmetrize the results.