de Sitter Black Holes as Constrained States in the Euclidean Path Integral

TL;DR

This paper demonstrates that Schwarzschild-de Sitter black holes can be understood as constrained saddle points in the Euclidean path integral, enabling a consistent calculation of their probability in de Sitter space despite horizon temperature differences.

Contribution

It introduces a constrained Euclidean path integral framework that incorporates Schwarzschild-de Sitter black holes as legitimate saddle points.

Findings

Schwarzschild-de Sitter black holes are saddle points in a constrained Euclidean path integral.

The probability of finding a black hole in de Sitter space is computed as ^{-(S_{dS}-S_{SdS})}.

Provides a new perspective on black hole thermodynamics in de Sitter space.

Abstract

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 SdS is a genuine saddle point of a certain constrained path integral, providing a consistent Euclidean computation of the probability $\sim e^{-(S_{dS}-S_{SdS})}$ to find a black hole in the de Sitter bath.