de Rham wave equation for tensor valued p-forms

The de Rham Laplacian $\Delta_{\rm (dR)}$ for differential forms is a geometric generalization of the usual covariant Laplacian $\Delta$, and it may be extended naturally to tensor-valued $p$-forms using the exterior covariant derivative associated with a metric connection. Using it the wave equation satisfied by the curvature tensors in general relativity takes its most compact form. This wave equation leads to the Teukolsky equations describing integral spin perturbations of black hole spacetimes.