X-Nico

Tetradic Palatini action

which, after multiplication by $e\; \{I\; \backslash beta\}$ just tells us that the Einstein tensor $R\; \{\backslash alpha\; \backslash beta\}\; -\; \{1\; \backslash over\; 2\}\; R\; g\; \{\backslash alpha\; \backslash beta\}$ of the metric defined by the tetrads vanishes.

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Another important action is the Plebanski action (see the entry on the Barrett-Crane model), and proving that it gives general relativity under certain conditions involves showing it reduces to the Palatini action under these conditions.

see also