Baby de Sitter Black Holes and dS$_3$/CFT$_2$

TL;DR

This paper explores three-dimensional de Sitter black holes in massive gravity, demonstrating their thermodynamic properties and the realization of dS/CFT correspondence through asymptotic symmetries and holographic techniques.

Contribution

It shows that dS black holes in massive gravity have a conformal symmetry at infinity and their entropy matches CFT predictions, advancing the understanding of dS/CFT.

Findings

Asymptotic symmetry group matches 2D conformal algebra.

Virasoro algebra with non-zero central charge found.

Black hole entropy matches Cardy's formula.

Abstract

Unlike three-dimensional Einstein gravity, three-dimensional massive gravity admits asymptotically de Sitter space (dS) black hole solutions. These black holes present interesting features and provide us with toy models to study the dS/CFT correspondence. A remarkable property of these black holes is that they are always in thermal equilibrium with the cosmological horizon of the space that hosts them. This invites us to study the thermodynamics of these solutions within the context of dS/CFT. We study the asymptotic symmetry group of the theory and find that it indeed coincides with the local two-dimensional conformal algebra. The charge algebra associated to the asymptotic Killing vectors consists of two copies of the Virasoro algebra with non-vanishing central extension. We compute the mass and angular momentum of the dS black holes and verify that a naive application of Cardy's formula exactly reproduces the entropy of both the black hole and the cosmological horizon. By adapting the holographic renormalization techniques to the case of dS space, we define the boundary stress tensor of the dual Euclidean conformal field theory.