A de Sitter Hoedown

TL;DR

This paper thoroughly analyzes rotating black holes in de Sitter space, exploring their thermal phase structure, wave dynamics, and holographic dualities, highlighting the unique rotating Nariai limit where horizons are in equilibrium.

Contribution

It provides a complete description of the thermal phases of rotating de Sitter black holes and investigates the wave equation and holographic aspects of the rotating Nariai geometry.

Findings

Identified the rotating Nariai limit with horizons in thermal and rotational equilibrium.

Computed the scalar wave absorption cross section and superradiance conditions.

Derived quasinormal modes and boundary correlators, supporting holographic duality.

Abstract

Rotating black holes in de Sitter space are known to have interesting limits where the temperatures of the black hole and cosmological horizon are equal. We give a complete description of the thermal phase structure of all allowed rotating black hole configurations. Only one configuration, the rotating Nariai limit, has the black hole and cosmological horizons both in thermal and rotational equilibrium, in that both the temperatures and angular velocities of the two horizons coincide. The thermal evolution of the spacetime is shown to lead to the pure de Sitter spacetime, which is the most entropic configuration. We then provide a comprehensive study of the wave equation for a massless scalar in the rotating Nariai geometry. The absorption cross section at the black hole horizon is computed and a condition is found for when the scattering becomes superradiant. The boundary-to-boundary correlators at finite temperature are computed at future infinity. The quasinormal modes are obtained in explicit form. Finally, we obtain an expression for the expectation value of the number of particles produced at future infinity starting from a vacuum state with no incoming particles at past infinity. Some of our results are used to provide further evidence for a recent holographic proposal between the rotating Nariai geometry and a two-dimensional conformal field theory.