Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about the metric tensor in Einstein's field equations.

  1. Aug 11, 2004 #1
    I was wonder if some can explain to me what exactly are the 10 parameters for the metric tensors. I know the reason for getting 10 parameters, 3^2=9 + 1, you get three for every spatial dimensions plus one for time. But why exactly three parameters for each spatial dimension? And what exactly are these three parameters for a spatial dimension? Can someone fill me in, I really what to know! :biggrin:
  2. jcsd
  3. Aug 12, 2004 #2


    User Avatar
    Science Advisor

    If you remember that the metric tensor is symmetric and rank-2, then in a spacetime with T dimensions of time and S dimensions of space, the number of independent elements of the metric (or "parameters" as you call them) is (T+S)(T+S+1)/2. For our particular universe, that works out to 4*5/2 = 10.
  4. Aug 12, 2004 #3
    Yes I know. But what exaclty does each element represent? Like in a vector you have distance in the xyz directions. In a tensor I assume three of the elements are just distances in xyz but what about the other 6 elements? Sorry I'm trying to explain my question as best I can.
  5. Aug 12, 2004 #4


    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    The i-j element in the metric tensor is the coefficient of the dxidxj term in the general version of Pythagoras' rule. The tensor is symmetric because the multiplication is commutative, and dxidxj = dxjdxi.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook