Holography at an Extremal De Sitter Horizon

TL;DR

We address the problem of microscopic quantum gravity descriptions for de Sitter horizons by analyzing extremal rotating Kerr--de Sitter black holes in the Nariai limit. The rotating Nariai geometry yields a Virasoro asymptotic symmetry with a real, positive central charge and, together with a left-moving temperature, reproduces the cosmological horizon entropy via the Cardy formula, suggesting a Euclidean 2D CFT dual. This framework parallels Kerr/CFT but applies to a cosmological horizon with a fiber over $dS_2$, offering a concrete holographic perspective for de Sitter horizons while noting potential non-unitarity in the dual. The results motivate further tests, including charged generalizations, higher-dimensional extensions, and stability/instability analyses to sharpen the bulk–CFT dictionary.

Abstract

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS_2 rather than AdS_2.

Figures (1)

• Figure 1: Penrose diagram of $dS_2$ with the cosmological horizons explicit. The left and right sides are identified.