Causal structures of pp-waves

TL;DR

This paper investigates the causal structure of pp-wave spacetimes, extending previous work to include specific backgrounds like the N=2 sine-Gordon string, revealing their geodesic completeness and causal boundary dimensions.

Contribution

It generalizes the causal boundary analysis of pp-waves, including specific models like the N=2 sine-Gordon background, using the ideal point construction.

Findings

The pp-wave spacetime with N=2 sine-Gordon string is geodesically complete.

This spacetime has a one-dimensional causal boundary.

The work extends causal boundary analysis to new classes of pp-waves.

Abstract

We discuss the causal structure of pp-wave spacetimes using the ideal point construction outlined by Geroch, Kronheimer, and Penrose. This generalizes the recent work of Marolf and Ross, who considered similar issues for plane wave spacetimes. We address the question regarding the dimension of the causal boundary for certain specific pp-wave backgrounds. In particular, we demonstrate that the pp-wave spacetime which gives rise to the N = 2 sine-Gordon string world-sheet theory is geodesically complete and has a one-dimensional causal boundary.