Varying Minkowski Metric: Is {\delta}{\eta}_{\mu\nu}=0?

[Physicist97]

So I was wondering, is the variation of the Minkowski Metric zero? As in ${\delta}{\eta}_{\mu\nu}=0$ . I would think this is the case because the components of the Minkowski Metric are just numbers (either +1 or -1), so varying it gives you 0. Is this correct?

 

[Noctisdark]

What do you mean ? η_μν is just and bunch of zero and +/- 1 every where, so normally it's differential is equal to zero !

 

[Physicist97]

Right, well that's what I was asking haha. I just needed some reassurance that it was the correct answer, thank you.