Stability of the microcanonical ensemble in Euclidean Quantum Gravity

A bstract This work resolves a longstanding tension between the physically-expected stability of microcanonical ensemble for gravitating systems and fact that known negative mode asymptotically flat Schwarzschild black hole decays too rapidly at infinity to affect ADM energy boundary term infinity. The key our study is we fix an appropriate off-shell notion energy, which obtain by constructing partition function as integral transform canonical function. After applying rule-of-thumb Wick rotations from recent companion paper deal with conformal problem Euclidean gravity, find positive definite action linear perturbations about any Schwarzchild (-AdS) hole. Most done in cavity reflecting conditions, but wall can be removed taking limit.