Motivated by a possible quantum gravity construction, Penrose has shown that, despite being asymptotically flat, there is an inconsistency between the causal structure at infinity of Schwarzschild and Minkowski spacetimes. However, the proof of this inconsistency is specific to 4 spacetime dimensions. In this talk I will discuss how this result extends to higher (and lower) dimensions. More generally, I will consider examples of how the causal structure of asymptotically flat spacetimes are affected by dimension and by the presence of mass (both positive and negative). I will then show how these ideas can be used to prove a higher dimensional extension of the positive mass theorem of Penrose, Sorkin and Woolgar.
