- #1
Pencilvester
- 196
- 46
In Carroll’s “Spacetime and Geometry” his equation (1.116) for ##\partial_{\mu} T^{\mu \nu}## for a perfect fluid ends with the term ##... + ~\partial^{\nu} p##. First of all, in order for this equation to really be general, it would need to use the covariant derivative instead of the simple partials, right? I assume he’s assuming a flat Minkowski spacetime where dels work just fine because it’s at the beginning of the book. But here’s the main question: is ##\partial^{\nu} p## just the same as ##\eta^{\nu \sigma} \partial_{\sigma} p## here? I’ve just never seen a del with a superscript before, and he offers no explanation for it.