Hertzian gravitational potentials for type D space–times

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Abstract
Hertzian gravitational potentials for type D vacuum space–times are defined. The Geroch–Held–Penrose formalism is expressed in the language of exterior forms, and by using its formal simplifications, the existence of Hertzian potentials for this class of nonlinear gravitational fields is demonstrated. The explicit form of these potentials possessing the spin and boost weights and the self‐dual property of the field 2‐form is constructed. The gauge freedom associated with these potentials is discussed, and the procedure is found to resemble the Debye reduction of the electromagnetic Hertzian potentials in that it enables us to construct a complex scalar superpotential from the Weyl spinor.

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