I am a bit confused at "orthonormal tetrad" in General Relativity...

[Junjie]

I think orthonormal tetrad should be a set of vectors like

e0= (1,0,0,0)
e1= (0,1,0,0)
e2= (0,0,1,0)
e3= (0,0,0,1)


However, in my book, it is written as

e0= (-1,0,0,0)
e1= (0,1,0,0)
e2= (0,0,1,0)
e3= (0,0,0,1)



I am not sure which one is right, and why it is right. My roomate think both are right, which makes me even more confused.

[Bill_K]

Your second tetrad is obtained from your first by reflecting e0. Both are correct. You could say that one set is right-handed and the other set is left-handed (if you had four-dimensional hands)