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2015

On covariant expansion of the gravitational St\"{u}ckelberg trick

Gao, Xian

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A new approach to expanding the "St\"{u}ckelbergized" fiducial metric in a covariant manner is developed.

The idea is to consider the curved 4-dimensional space as a codimension-one hypersurface embedded in a 5-dimensional Minkowski bulk, in which the 5-dimensional Goldstone modes can be defined as usual.
After solving one constraint among the five 5-dimensional Goldstone modes and projecting onto the 4-dimensional hypersurface, we are able to express the "St\"{u}ckelbergized" fiducial metric in terms of the 4-dimensional Goldstone modes as well as 4-dimensional curvature quantities.
We also compared the results with expressions got using the Riemann Normal Coordinates (RNC) in Gao et al [Phys.

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