Charges, complex structures, and perturbations of instantons

Abstract

Hermitian non-Kähler 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.

v4: The original paper has been divided into two separate submissions to improve clarity and focus. The present submission is devoted to linearized charges for perturbations of gravitational instantons, while a companion paper establishes infinitesimal rigidity and integrability of the moduli space