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43 - Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
from Part III - Other Spins or Statistics; General Relativity
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 405-417
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Summary

We define the only example of fully linear general relativity, for plane parallel (pp waves), where the Einstein equation reduces to a Poisson equation. We show, according to Penrose, that in the “Penrose limit,” when focusing in near a null geodesic, we find a pp wave. We show how to go between the “Rosen coordinates” and “Brinkmann coordinates” for the pp wave and give an example of the Penrose limit. Gravitational shockwaves are defined in flat space, leading to the Aichelburg–Sexl metric. General shock waves, shock waves generated by a graviton, and shockwaves in other backgrounds, are defined. We end with the Khan–Penrose interacting solution for two colliding shock waves.