A Hierarchy of Spacetime Symmetries: Holes to Heraclitus.
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 th...
| Publicado en: | British Journal for the Philosophy of Science Vol. 77; no. 3; pp. 621 - 643 |
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| Autores principales: | , |
| Formato: | Artículo |
| Publicado: |
University of Chicago Press
Sep2026
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| Acceso en línea: | Ver este registro en EBSCOhost |
| Sumario: | 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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