Manchak, JB and Barrett, Thomas William (2023) A Hierarchy of Spacetime Symmetries: Holes to Heraclitus. [Preprint]
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Abstract
We present a hierarchy of symmetry conditions within the context of general relativity. The weakest condition captures a sense in which spacetime is free of symmetry "holes" of a certain type. All standard models of general relativity satisfy the condition but we show that violations can occur if the Hausdorff assumption is dropped. On the other extreme, the strongest condition of the hierarchy is satisfied whenever a model is completely devoid of symmetries. In these "Heraclitus" spacetimes, no pair of distinct points can be mapped (even locally) into one another. We prove that such spacetimes exist. We also show a sense in which Heraclitus spacetimes are completely determined by their local properties. We close with a brief comment on the prospect of using the symmetries of a spacetime as a guide to how much "structure" it possesses.
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| Item Type: | Preprint | |||||||||
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| Keywords: | Spacetime, Symmetries, Structure | |||||||||
| Subjects: | Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | John Byron Manchak | |||||||||
| Date Deposited: | 09 Aug 2023 13:51 | |||||||||
| Last Modified: | 09 Aug 2023 13:51 | |||||||||
| Item ID: | 22381 | |||||||||
| Subjects: | Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 8 August 2023 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/22381 |
Available Versions of this Item
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A Hierarchy of Spacetime Symmetries: Holes to Heraclitus. (deposited 03 Sep 2022 19:14)
- A Hierarchy of Spacetime Symmetries: Holes to Heraclitus. (deposited 09 Aug 2023 13:51) [Currently Displayed]
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