Timelike Metrics: What Is a Timelike Vector?

[pleasehelpmeno]

In a given metric say Scwarzchild is $\frac{\partial}{\partial t}$ time-like when the coefficient in front of the dxdx term is <0 and space-like when the coefficients in front of spatial terms >0 ?

and what is a timelike vector is it simply a vector in the coefficient that satisfies the above criteria?

 

[PAllen]

In a given metric say Scwarzchild is $\frac{\partial}{\partial t}$ time-like when the coefficient in front of the dxdx term is <0 and space-like when the coefficients in front of spatial terms >0 ?

and what is a timelike vector is it simply a vector in the coefficient that satisfies the above criteria?

Are you talking about the killing vector? That's the abbreviated notation normally used for it. You see that it is a killing vector in this case because it makes all the metric components vanish. You see that it is timelike or spacelike by the sign of gtt.

 

[WannabeNewton]

Are you talking about the killing vector? That's the abbreviated notation normally used for it. You see that it is a killing vector in this case because it makes all the metric components vanish. You see that it is timelike or spacelike by the sign of gtt.

I believe he is talking about the basis vector that is dual to $dt$ i.e. $dt(\partial t) = 1$. This is very coordinate chart specific but yes as PAllen already stated it is based on the sign of gtt. In general on a space - time M, at $p\in M$ some $v\in T_{p}(M)$ is time - like if $g_{p}(v,v) < 0$ using the -+++ convention.