Conformal boundary and geodesics for $AdS_5\times S^5$ and the plane wave: Their approach in the Penrose limit

TL;DR

This paper explores the relationship between the conformal boundaries and geodesics of $AdS_5\times S^5$ and plane waves via the Penrose limit, revealing how null geodesics and their boundaries transform in this limit.

Contribution

It provides a detailed geometric analysis of how conformal boundaries and geodesics behave under the Penrose limit from $AdS_5\times S^5$ to plane waves.

Findings

Conformal boundaries of $AdS_5\times S^5$ and plane waves coincide in the Penrose limit.

Null geodesics form a degenerating cone in the limit.

Geodesic structures are explicitly constructed and analyzed.

Abstract

Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.