A survey showing that stability and infinitesimal deformability of Einstein metrics both reduce to the spectrum of the Lichnerowicz Laplacian, with a compendium of known results and open questions.
Instability of conformally K\"ahler, Einstein metrics
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abstract
We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not hyperK\"ahler and to the Chen-Lebrun-Weber metric in particular.
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Einstein metrics, their moduli spaces and stability
A survey showing that stability and infinitesimal deformability of Einstein metrics both reduce to the spectrum of the Lichnerowicz Laplacian, with a compendium of known results and open questions.