Charges, complex structures, and perturbations of instantons

Abstract

Hermitian non-K\"ahler Einstein 4-manifolds have a quasi-locally conserved charge associated to spin-lowering via Killing spinors, and corresponding to a parameter of the moduli space. This charge is evaluated for all explicitly known examples of gravitational instantons. Generic gravitational perturbations are shown to admit a closed 2-form that measures the perturbation to this charge, generalizing previous Lorentzian results on the linearized mass of perturbed Kerr black holes.