A de Sitter Hoedown

TL;DR

The paper investigates rotating Kerr–de Sitter black holes, focusing on the rotating Nariai limit where the black hole and cosmological horizons share the same temperature and angular velocity. It demonstrates that this equilibrium is thermodynamically unstable and that the spacetime evolves toward pure de Sitter space as the most entropic state. The authors solve the massless scalar wave equation in the rotating Nariai geometry, obtaining explicit quasinormal modes, absorption cross-sections, and cosmological particle production, and they compute finite-temperature boundary correlators, finding structures consistent with a two-dimensional conformal field theory at future infinity. Evidence for a rotating Nariai/CFT holographic correspondence is presented through matching asymptotic symmetries and correlator poles to a 2D Euclidean CFT, with left and right moving sectors and corresponding temperatures $T_L$ and $T_R$. These results illuminate quantum aspects of de Sitter holography and suggest further exploration of holographic duals in cosmological spacetimes.

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.

Figures (6)

• Figure 1: The physically allowed configurations for Kerr-de Sitter space. We are using units where $\ell = 1$.
• Figure 2: (a): Phase space of allowed solutions in the $(r_+,a)$-plane. Above the green (dotted) line, the black hole horizon has negative specific heat. The red (solid) line indicates the lukewarm configurations. (b): Constant $J$ curves in the $(r_+,a)$-plane. We are plotting in units where $\ell = 1$.
• Figure 3: (a): Regions of negative $\partial S_{BH}^2/\partial J^2$ below the green (dotted) curve. (b): Constant $E$ curves in the $(r_+,a)$-plane. We are plotting in units where $\ell = 1$.
• Figure 4: Contour plot of constant total entropy curves. The direction of increasing entropy is toward the origin of the configuration space, i.e. pure de Sitter space. We plot in units where $\ell = 1$.
• Figure 5: (a): Thermal evolution when emission of energy is suppressed. (b): Thermal evolution when emission of angular momentum is suppressed.