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Find tetrad component from metric

  1. Dec 26, 2012 #1
    How can find components of tetrads from metric ?
    i know the relation between tetrads and metric
    g[itex]_{μ \nu}[/itex]=η[itex]_{ab}[/itex]e[itex]^{a}_{μ}[/itex]e[itex]^{b}_{\nu}[/itex]
    where e[itex]^{b}_{\nu}[/itex] are component of tetrads , in the case of Schwarzschild that metric is diagonal , it is a easy problem but what about non-diagonal metric like kerr ?
    Last edited: Dec 26, 2012
  2. jcsd
  3. Dec 26, 2012 #2

    George Jones

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    Consider the metric as a 4x4 symmetric matrix. Diagonalize this matrix.
  4. Dec 26, 2012 #3
    if we do that we get lorentz metric !!
  5. Dec 26, 2012 #4
    u mean find eigen vectors ?
  6. Dec 27, 2012 #5


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    gμν = ηabeaμebν

    Write this as a matrix equation:

    gμν = eaμ ηab ebν

    g = eT η e

    The tetrad components form the matrix necessary to transform g into η.
  7. Dec 27, 2012 #6
    Thank u dude !
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