Ricci-flat spacetimes with l-conformal Galilei symmetry

TL;DR

This paper constructs Ricci-flat ultrahyperbolic metrics with l-conformal Galilei symmetry, revealing their relation to AdS_2 geometries and analyzing the dynamics of geodesic equations with independent acceleration generators.

Contribution

It introduces new Ricci-flat metrics with l-conformal Galilei symmetry involving AdS_2, and studies their geodesic equations and dynamical properties.

Findings

Metrics involve AdS_2 in a manner similar to near horizon black hole geometries.

Geodesic equations form a second order dynamical system.

Acceleration generators are functionally independent.

Abstract

Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations are shown to describe a second order dynamical system for which the acceleration generators are functionally independent.