The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box

A bstract We revisit the stability of black hole saddles for Euclidean path integral describing canonical partition function Z ( β ) gravity inside a spherical reflecting cavity. The boundary condition at cavity wall couples transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Schwarzschild holes in infinite-volume asymptotically flat asymototically AdS spacetimes. This coupling obstructs familiar Gibbons-Hawking-Perry treatment conformal factor problem, as Wick rotation would require TT be rotated well. also leads complex eigenvalues Lichnerowicz operator. nevertheless find operator can diagonalized space coupled modes. observation allows eigenmodes define natural generalization Wick-rotation recipe infinite volume, with result mode eigenvalue λ is stable when Re > 0. In any cavity, cosmological constant Λ ≤ 0, we show this reproduce expectation from thermodynamics large while defined by small unstable.