Timelike metrics

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?

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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.

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