Error in Carroll's Lecture Notes on General Relativity pg. 186

[maxverywell]

Mistake in Carroll's Notes?

On the page 186 of Lecture Notes on General Relativity, where he writes the line element in both $\tilde{u}$ and $\tilde{v}$ coordinates , I think he missed a minus sign. Can someone check it, please?

Also, why he writes $(d\tilde{u} d\tilde{v}+d\tilde{v}d\tilde{u})/2$ instead of $d\tilde{u} d\tilde{v}$?

 

[Samshorn]

On the page 186 of Lecture Notes on General Relativity, where he writes the line element in both $\tilde{u}$ and $\tilde{v}$ coordinates , I think he missed a minus sign. Can someone check it, please?

Yes, that's a typo. The first term in equation 7.73 on page 186 should be negative.