On the Existence of Radiation Gauges in Petrov Type II Spacetimes

The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four (which we treat here as) ``gauge'' conditions plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition --- on a particular tetrad component of the stress-energy tensor --- under which one can impose the full IRG/ORG. In a Petrov type II background, imposing the IRG/ORG requires (consistently) setting a particular component of the metric perturbation to zero ``by hand.'' By contrast, in a generic type D background, gauge freedom can generally be used to achieve this. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. If time permits, implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacetimes will be briefly discussed.