Conformal boundary and geodesics for AdS₅× S⁵ and the plane wave: Their approach in the Penrose limit

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Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of AdS₅× S⁵ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all AdS₅× S⁵ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of AdS₅× S⁵ to that of the plane wave is studied in detail. At each point these null geodesics of AdS₅× S⁵ form a cone which degenerates in the limit.