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2018

Symmetries of first-order Lovelock gravity

Montesinos, Merced, Romero, Rodrigo, Díaz, Bogar

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We apply the converse of Noether's second theorem to the first-order $n$-dimensional Lovelock action, considering the frame rotation group as both $SO\left(1,n-1\right)$ or as $SO(n)$.

As a result, we get the well-known invariance under local Lorentz transformations or $SO(n)$ transformations and diffeomorphisms, for odd- and even-dimensional manifolds.
We also obtain the so-called `local translations' with nonvanishing constant $\Lambda$ for odd-dimensional manifolds when a certain relation among the coefficients of the various terms of the first-order Lovelock Lagrangian is satisfied.
When this relation is fulfilled, we report the existence of a new gauge symmetry emerging from a Noether identity.

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