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Timelike metrics

  1. Jan 29, 2013 #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?
  2. jcsd
  3. Jan 29, 2013 #2


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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.
  4. Jan 29, 2013 #3


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    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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