Twofold Symmetries of the Pure Gravity Action

Understand

We recast the action of pure gravity into a form that is invariant under a twofold Lorentz symmetry.

• To derive this representation, we construct a general parameterization of all theories equivalent to the Einstein-Hilbert action up to a local field redefinition and gauge fixing.
• We then exploit this freedom to eliminate all interactions except those exhibiting two sets of independently contracted Lorentz indices.
• The resulting action is local, remarkably simple, and naturally expressed in a field basis analogous to the exponential parameterization of the nonlinear sigma model.