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Components of gab metric

  1. Aug 27, 2014 #1

    I am trying to understand Kaluza Klein theory on the five dimensional unification. It was mentioned over there:

    " Of the 15 components of gαβ, five had to get a new physical interpretation, i.e. gα5 and g55; the components gik, i,k = 1,...,4, were to describe the gravitational field as before; Kaluza took gi5 proportional to the electromagnetic vector potential Ai"

    My question is that gαβ, if I take the metric tensor of general relativity has 16 components (g00.....g33). Can anybody please clarify?

  2. jcsd
  3. Aug 27, 2014 #2


    Staff: Mentor

    Due to symmetry only 10 of the 16 components are independent. Similarly, although adding a 5th dimension gives 9 more components, only 5 are independent.
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