Abstract
We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang-Mills--like Lagrangian of metric-affine gravity (MAG), the gauge theory of the general affine group in the presence of a metric. Because of the geometric character of MAG, this can best be seen by using Vasiliev's frame formalism for higher-spin gauge fields in which the spin-3 frame is identified with the tracefree nonmetricity one-form associated with the shear generators of $GL(n,\mathbb{R})$. Furthermore, for specific gravitational gauge models in the framework of full nonlinear MAG, exact solutions are constructed, featuring propagating massless and massive spin-3 fields.
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