Notation: Partial derivative with two indices. What does it stand for

Question

I am reading in the book, Gravity from Eric Poisson and Clifford M. Will, and they use a notation of a partial derivative operator with two indices, eg $\partial_{ij}$.

I am sure they must have introduced it somewhere – but I cannot find it.

Is it a standard notation, and if so, what does it mean?

Thanks for help!

Answer 1

It might mean a second derivative with respect to the standard coordinates with those indices, i.e., $$\partial_{ij} f(x_1, \dots, x_n) = \frac{\partial}{\partial x_j} \frac{\partial}{\partial x_i} f(x_1, \dots, x_n).$$ Of course, the book might define it in some other way than this, but off the top of my head, this is the only reasonably common usage I can think of.