Timelike metrics

  • #1
In a given metric say Scwarzchild is [itex]\frac{\partial}{\partial t}[/itex] 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?
 

Answers and Replies

  • #2
PAllen
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In a given metric say Scwarzchild is [itex]\frac{\partial}{\partial t}[/itex] 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.
 
  • #3
WannabeNewton
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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 [itex]dt[/itex] i.e. [itex]dt(\partial t) = 1[/itex]. 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 [itex]p\in M[/itex] some [itex]v\in T_{p}(M)[/itex] is time - like if [itex]g_{p}(v,v) < 0[/itex] using the -+++ convention.
 

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