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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.02492 |
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| _version_ | 1866917360390111232 |
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| author | Moncrief, Vincent Rieger, Nathalie E. |
| author_facet | Moncrief, Vincent Rieger, Nathalie E. |
| contents | We propose an extension of basic Kaluza-Klein theory in which the higher-dimensional Lorentzian manifold develops a Cauchy horizon rather than remaining globally hyperbolic as in the conventional framework. In this setting, the $U(1)$-generating Killing field, assumed to exist in Kaluza-Klein theory, undergoes a transition in its causal character, from spacelike in the globally hyperbolic region to timelike in an acausal extension through a horizon. This yields a (lower-dimensional) quotient manifold whose metric changes signature from Lorentzian to Riemannian. In this way, one observes a singular, signature changing transition emerging rather naturally from the projection of a globally smooth, even analytic, Lorentzian geometry ``up in the bundle''. This reveals a ``signature change without signature change'' scenario -- a phrasing inspired by John Wheeler -- and extends the usual Kaluza-Klein framework in a conceptually natural direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Conceptual Introduction To Signature Change Through a Natural Extension of Kaluza-Klein Theory Moncrief, Vincent Rieger, Nathalie E. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We propose an extension of basic Kaluza-Klein theory in which the higher-dimensional Lorentzian manifold develops a Cauchy horizon rather than remaining globally hyperbolic as in the conventional framework. In this setting, the $U(1)$-generating Killing field, assumed to exist in Kaluza-Klein theory, undergoes a transition in its causal character, from spacelike in the globally hyperbolic region to timelike in an acausal extension through a horizon. This yields a (lower-dimensional) quotient manifold whose metric changes signature from Lorentzian to Riemannian. In this way, one observes a singular, signature changing transition emerging rather naturally from the projection of a globally smooth, even analytic, Lorentzian geometry ``up in the bundle''. This reveals a ``signature change without signature change'' scenario -- a phrasing inspired by John Wheeler -- and extends the usual Kaluza-Klein framework in a conceptually natural direction. |
| title | A Conceptual Introduction To Signature Change Through a Natural Extension of Kaluza-Klein Theory |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2510.02492 |