Holography For a De Sitter-Esque Geometry

TL;DR

This paper explores warped dS3 geometries in topologically massive gravity, analyzing their thermodynamics, asymptotic symmetries, and potential holographic duals, revealing unique features like unbounded entropy and specific symmetry structures.

Contribution

It introduces and studies warped dS3 solutions in TMG, detailing their thermodynamic properties, asymptotic symmetries, and discussing their holographic interpretation.

Findings

Warped dS3 solutions have both cosmological and internal horizons.

Their entropy can be arbitrarily large, unlike standard de Sitter black holes.

Asymptotic symmetry group includes a Virasoro and a current algebra, with a vanishing right-moving central charge at specific parameters.

Abstract

Warped dS$_3$ arises as a solution to topologically massive gravity (TMG) with positive cosmological constant $+1/\ell^2$ and Chern-Simons coefficient $1/\mu$ in the region $\mu^2 \ell^2 < 27$. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS$_3$ asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when $\mu^2 \ell^2 = 27/5$. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.