Sailing from Warped AdS_3 to Warped dS_3 in Topologically Massive Gravity

TL;DR

This paper explores warped AdS_3 and dS_3 solutions in topologically massive gravity across different cosmological constants, revealing new geometries, horizons, and superradiance phenomena with potential holographic implications.

Contribution

It extends the holographic duality proposal to positive and zero cosmological constants, discovering new warped dS_3 solutions and analyzing scalar wave behavior.

Findings

Warped dS_3 solutions with horizons and Hawking temperature

Scalar superradiance indicating Schwinger pair production

Global identifications leading to additional horizons

Abstract

Three-dimensional warped anti-de Sitter space in topologically massive gravity with a negative cosmological constant has been proposed to be holographically dual to a two-dimensional conformal field theory. We extend this proposal to both positive and vanishing values of the cosmological constant where stretched warped anti-de Sitter space is found to be a solution. For positive cosmological constant, another class of warped solutions is obtained by a spacelike (timelike) line fibration over Lorentzian (Euclidean) two-dimensional de Sitter space. These solutions exhibit a cosmological horizon and Hawking temperature much like de Sitter space. Global identifications of this warped de Sitter space may contain a horizon in addition to the cosmological one. At a degenerate point, warped de Sitter space becomes a fibration over two-dimensional flat space. Finally, we study scalar waves in these backgrounds. Scalars in stretched warped anti-de Sitter space exhibit superradiance which can be interpreted as Schwinger pair production of charged particles in two-dimensional anti-de Sitter space.