 Ultrarelativistic limit of the boosted Schwarzschild metric away from the null plane

Boost a Schwarzschild mass with speed $v$ and hold $p=m\gamma$ fixed as $v\to 1$. Away from the null plane $x=t$, the isotropic-coordinate expression tends toThe complete distributional limit on the null plane requires the additional coordinate treatment that produces the Aichelburg-Sexl shock wave.