Recent content by kparchevsky

>I don't get why you use "covariant coordinates" in the first place The goal was to prove the specific formula in the specific book, and this formula was written in covariant coordinates.

Thank you. Trying to prove Eq.(8) I took differential from both sides of Eq.(6), solved it for ##dx^i##, converted it to ##dx_i##, plugged into Eq.(7) and zeroed term at ##dx'^i dx'^j##, but I just had to use the definition of a tensor! The rest of derivation in the book is clear.

In the very first term (and in the whole expression), don't indices mu and nu should be on different levels like -1/2 d_\nu g_\mu^a d^\nu g^{\mu a}?

In page 67 of book "The mathematical theory of black holes" by S. Chandrasekhar in chapter 2 "Space-Time of sufficient generality" there is a theorem that metric of a 2-dimensional space $$ds^2 = g_{11} (dx^1)^2 + 2g_{12} dx^1 dx^2 + g_{22} (dx^2)^2$$ can be brought to a diagonal form. I would...