Could someone please explain briefly the advantange of doing GR in terms of the tetrad field instead of the metric?(adsbygoogle = window.adsbygoogle || []).push({});

A little background for the beginners who may be reading. As originally formulated by Einstein the dynamical quantify of GR is the spacetime metric [tex]g_{\mu\nu}(x)[/tex]. One can introduce quantities called a tetrad field [tex]e^{I}_{\mu}(x)[/tex] such that

[tex]e^{I}_{\mu}e^{J}_{\nu}\eta_{IJ}=g_{\mu\nu}[/tex]

everywhere, where [tex]\eta_{IJ}[/tex] is the flat Minkowski metric. Then you rewrite all the GR equations in terms of [tex]e^{I}_{\mu}(x)[/tex].

But we have introduced extra degrees of freedom. Any two tetrad fields related by a (local?) Lorentz transformation are equivalent. Why would we want to do that?

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# Why use the tetrad formalism?

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