Why does the timelike vector in an orthonormal tetrad have -1?

[Junjie]

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

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)