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Geodesic deviation in 2d

  1. May 6, 2015 #1
    In 2 dimensions, is the geodesic deviation equation governed by a single scalar, independent of the direction of the geodesics? That is, if ξ is the separation of two nearby geodesics, do we have [tex]d^2 \xi/ds^2 + R\xi = 0 [/tex] where R is a scalar that is completely independent of the direction of the geodesics?

    If so, how can we see that there can be no directional dependence in 2d?
     
  2. jcsd
  3. May 7, 2015 #2

    Mentz114

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    Gold Member

    By 2D do you mean ##t,x## ? So if you have a metric ##ds^2=-g_{00} dt^2 + g_{11}dx^2##, can you work it out explicitly ? If the velocities of the geodesics depend on ##t## or ##x##, is that directional dependence ?
     
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