The Canonical Ensemble Reloaded: The Complex-Stability of Euclidean quantum gravity for Black Holes in a Box

Understand

We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function $Z(\beta)$ for gravity inside a spherical reflecting cavity.

• The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Euclidean Schwarzschild black holes in infinite-volume asymptotically flat and asymototically AdS spacetimes.
• This coupling obstructs the familiar Gibbons-Hawking-Perry treatment of the conformal factor problem, as Wick rotation of the pure-trace modes would require that the TT modes be rotated as well.
• The coupling also leads to complex eigenvalues for the \L operator.