Is spacetime hole-free?

Abstract

Here, we examine hole-freeness-a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: Are all physically reasonable spacetimes hole-free?

Time Travel and Time Machines

“…61 We then have the following formulation of weak cosmic censorship: the maximal Cauchy development of generic, asymptotically flat initial data for Einstein's field equations with suitable matter fields has a complete I + . If weak cosmic censorship holds, it would imply that even if it is in principle possible to produce a singularity (even one that is not "benign" locally) by rearranging matter and energy within a finite region of spacetime, the effects of this singularity will not reach distant observers.…”

On the Possibility of Supertasks in General Relativity

“…Intuitively, this condition guarantees that, for any spacelike surface Σ, the set D + (Σ) is "as large as it can be". We note here, however, that it is not clear that all physically reasonable spacetimes are hole-free [12], [14]. But, even granting this assumption, it is not as if a no-go theorem is then straightforwardly obtained.…”

On Space-Time Singularities, Holes, and Extensions

“…But it turns out that under the assumption of global hyperbolicity, we find that inextendibility implies hole-freeness (Manchak 2009). It has been conjectured (Penrose 1979) that all physically reasonable spacetimes are globally hyperbolic.…”

“…But surprisingly, it turns out the definition is too strong; Minkowski spacetime fails to be hole-free under this formulation (Krasnikov 2009). But one can make minor modifications to avoid this consequence (Manchak 2009). …”