Randall-Sundrum Zero Mode as a Penrose Limit

TL;DR

This paper generalizes Penrose limits to include non-zero cosmological constants and demonstrates that Einstein spacetimes with certain symmetries limit to conformal plane waves, linking to Randall-Sundrum models.

Contribution

It introduces a new limiting procedure for spacetimes with non-zero cosmological constants, connecting Einstein spaces and brane world scenarios to plane wave limits.

Findings

Spacetimes with spacelike conformal Killing vectors have conformal plane wave limits.

Einstein spaces with non-positive cosmological constants have well-defined limits.

The nonlinear Randall-Sundrum zero mode emerges as a limit of brane world models.

Abstract

A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmological constant is negative or zero. When the conformal Killing vector is hypersurface orthogonal, the limits of Einstein spacetimes are certain AdS plane waves. In this case the nonlinear version of the Randall-Sundrum zero mode is obtained as the limit of the brane world scenarios.