On a Petrov-type D homogeneous solution

TL;DR

This paper introduces a new two-parameter family of solutions in 2+1 dimensional Einstein gravity with negative cosmological constant, obtained by squashing anti-de Sitter space, with implications for AdS/CFT correspondence.

Contribution

It presents a novel class of homogeneous solutions with four Killing vectors, including their global properties, higher-dimensional generalizations, and geodesic analysis.

Findings

New two-parameter family of solutions in 2+1D Einstein gravity.

Global embedding as intersection of quadratic surfaces in 7D.

Relevance to boundary geometries in AdS/CFT correspondence.

Abstract

We present a new two-parameter family of solutions of Einstein gravity with negative cosmological constant in 2+1 dimensions. These solutions are obtained by squashing the anti-de Sitter geometry along one direction and posses four Killing vectors. Global properties as well as the four dimensional generalization are discussed, followed by the investigation of the geodesic motion. A simple global embedding of these spaces as the intersection of four quadratic surfaces in a seven dimensional space is obtained. We argue also that these geometries describe the boundary of a four dimensional nutty-bubble solution and are relevant in the context of AdS/CFT correspondence.