I will be presenting some recent work at the next Southern California Philosophy of Physics Group meeting (Jan 14, 3:00pm, UC Irvine, SST 777).
Abstract: The Hawking-Penrose-Geroch singularity theorems tell us that (almost) all physically reasonable cosmological models are geodesically incomplete (i.e. they have “singularities”). On the other hand, a number of geodesically incomplete models seem to be artificial in various senses (e.g. they contain “holes” or have “extensions”). Two independent conditions — hole-freeness and inextendibility — serve to rule out some (but by no means all) of these seemingly artificial models. Here, I examine the relationship between these two conditions and the existence of singularities. First, I review what is known: geodesic completeness implies inextendibility. Next, I show that geodesic completeness also implies hole-freeness. (This answers a question posed by Geroch.) In addition, I introduce a simple intermediate condition — effective completeness — which is entailed by geodesic completeness and also entails both hole-freeness and inextendibility. Why might such a condition be of interest? It seems to be strong enough to rule out, in one fell swoop, both types of seemingly artificial models at issue here (and possibly other types as well) but weak enough to allow the more physically reasonable, geodesically incomplete models guaranteed by the singularity theorems. Finally, I show that under certain causality assumptions, there is a useful hierarchy of singularity types: geodesic completeness entails effective completeness which entails inextendibility which entails hole-freeness.