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Contravariant and Covariant Components GR versu SR

  1. Nov 10, 2014 #1
    I am trying to reconcile the definition of contravariant and covariant
    components of a vector between Special Relativity and General Relativity.

    In GR I understand the difference is defined by the way that the vector
    components transform under a change in coordinate systems.

    In SR it seems that it is more of a notational thing that allows for the
    derivation of the invariant interval.

    How are the 2 things related?
  2. jcsd
  3. Nov 10, 2014 #2


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    Staff: Mentor

    Do you have a source for the different treatment in SR? It can be made to look like it's just a notational thing in SR by using Minkowski coordinates where ##g_{\mu\rho}=g^{\mu\rho}## so many of the differences between contravariant and covariant components disappear - but that's just taking advantage of the fact that flat spacetime is an especially nice special case (which is why we call it "special" relativity).

    It's a good exercise to choose some perverse coordinate transform in which the metric acquires off-diagonal and non-constant components even in flat space-time, work a few otherwise-easy problems in those coordinates, just so that you can see the machinery working. You'll find that the contra/co distinction appears even in SR.
  4. Nov 10, 2014 #3
    OK, soon after I posted I realized that the connection is through the metric tensor.
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