On the Inextendibility of Space-Time

Abstract

It has been argued that spacetime must be inextendible -that it must be "as large as it can be" in some sense. Here, we register some skepticism with respect to this position.

General Relativity as a Collection of Collections of Models

“…A few non-local properties also render (**) true. 11 In particular, we have the following (see Manchak (2017) for a proof of the first of these results). One might be tempted to conclude from all of this that (**) will be true for any collection of 'physically reasonable' models.…”

“…Concerning (V ), things are still open as far as I know. If P = (W EC), we know that (*) is false (Manchak 2017). It turns out that the result can be generalized to include all of the standard energy conditions.…”

“…9 Upon this theorem rests a hefty philosophical weight. For one thing, it underpins the metaphysical justification for the ( †) position above (Earman 1995, Manchak 2017). For another, an influential definition of a 'singular' spacetime seems to depend on it (Geroch 1970).…”

Some Other “No Hole” Spacetimes Properties Are Unstable Too

“…This is bad news. As [6] (see also [14,15] for related remarks) had recently pointed out, most of the "no hole" conditions which have been proposed in the literature (see e.g. [16][17][18][19]) rely on mappings between a given spacetime and other spacetimes.…”

Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose

“…53 See Doboszewski [63,64] and Manchak [131,132] for conceptual studies of the (in)extendibility of space-times. 54 As pointed out to me by Julius Doboszewski, Chruściel et al [43] as well as Chruściel and Isenberg [42] only consider smooth extensions, so that looking at lower regularity seems a refinement postdating this early phase.…”