Warsaw Spacetime Colloquium #16 - JB Manchak (2021/05/28)
Channel: International Center for Formal Ontology
Date: 2021-05-29

Title: On the (In?)Stability of Spacetime Inextendibility

Chair: Antonio Vassallo

Abstract: Within the context of general relativity, the “stability” of various spacetime properties has been one important focus of study. It has been argued that “in order to be physically significant, a property of space-time ought to have some form of stability, that is to say, it should be a property of ‘nearby’ space-times” (Hawking and Ellis 1973, p. 197). Questions concerning the stability of spacetime properties are often made precise using the so-called “C^k fine” topologies on any collection of spacetimes with the same underlying manifold. (The property of “stable causality” is often defined using the C^0 fine topology.) Here we review what is known concerning the (in)stability of spacetime properties within this framework. After considering some foundational results concerning causal properties (Hawking 1969; Geroch 1970) and a fascinating drama concerning geodesic (in)completeness (Beem et al. 1996), we focus on the property of spacetime inextendibility about which very little is known. Because inextendibility is defined relative to a background “possibility space” in the form of a standard collection of spacetimes, one can naturally consider variant definitions relative to other collections. (Some formulations of the “cosmic censorship” conjecture rely on such variant definitions of inextendibility.) We find that the stability of “inextendibility” can be highly sensitive to the choice of definition — even when attention is limited to definitions that are relative to “physically reasonable” collections of spacetimes. Indeed, it is not yet clear that there is a physically significant sense in which “inextendibility” is a stable property. We close by drawing attention to some precise open questions which could be explored to clarify the situation.
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The Colloquium's goal is to provide a window into the state-of-the-art in the foundations of spacetime physics. It brings together top-level philosophers and physicists willing to share their current research with an international audience. The Colloquium is organized by the Philosophy of Physics Group at the International Center for Formal Ontology, Faculty of Administration and Social Sciences, Warsaw University of Technology.