Abstract
It is shown that there exists a one-to-one correspondence between the real solutions of the Einstein vacuum field equations linearized about the Minkowski metric and the (complex) metric perturbations whose curvature to first order in the metric perturbation is self-dual. It is also shown that the self-duality condition of the curvature to first order in the metric perturbation is equivalent to a set of first-order equations for the metric perturbation whose solution is given by a scalar potential that obeys the wave equation.
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