Probing Szekeres' colliding sandwich gravitational waves

The behavior of the Khan-Penrose impulsive plane colliding gravitational wave spacetime was investigated using the pseudo-Newtonian formalism, which expresses the spacetime curvature in terms of forces. The essential singularity produced after collision was seen as a rapid build-up of the force. However, the singularity, when either wave has passed before the collision, did not appear in the force, leading to the conclusion that it is a topological singularity. The question of whether this feature is an artefact of the impulsive wave or is inherent in the causal structure of the spacetime is investigated here by extending the analysis of the Szekeres colliding sandwich gravitational waves, and very interesting insights are obtained. In particular, what Szekeres called a coordinate singularity after the collision of the waves turns out to be a curvature singularity.

Automated summary

The behavior of the Khan-Penrose impulsive plane colliding gravitational wave spacetime was investigated, revealing a rapid build-up of force at the essential singularity after collision, while the singularity did not appear in the force before the waves passed, indicating a topological singularity. By extending the analysis to Szekeres colliding sandwich gravitational waves, it was found that what Szekeres called a coordinate singularity after the collision of waves turns out to be a curvature singularity.