de Sitter black holes as constrained states in the Euclidean path integral

Schwarzschild-de Sitter black holes have two horizons that are at different temperatures for generic values of the black hole mass. Since the horizons are out of equilibrium, the solutions do not admit a smooth Euclidean continuation, and it is not immediately clear what role they play in the gravitational path integral. We show that Euclidean Schwarzschild-de Sitter is a genuine saddle point of a certain constrained path integral, providing a consistent Euclidean computation of the probability similar to e-(S-dS-S-SdS) to find a black hole in the de Sitter bath.

Automated summary

Schwarzschild-de Sitter black holes have different-temperature horizons that play an important role in the gravitational path integral. Euclidean Schwarzschild-de Sitter serves as a genuine saddle point in a constrained path integral, allowing for the computation of the probability of finding a black hole in the de Sitter bath.