Quantum Spacetimes from General Relativity?
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913889685340160 |
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| author | Much, Albert |
| author_facet | Much, Albert |
| contents | We introduce a non-commutative product for curved spacetimes, that can be regarded as a generalization of the Rieffel (or Moyal-Weyl) product. This product employs the exponential map and a Poisson tensor, and the deformed product maintains associativity under the condition that the Poisson tensor $Θ$ satisfies $Θ^{μν}\nabla_νΘ^{ρσ}=0$, in relation to a Levi-Cevita connection. We proceed to solve the associativity condition for various physical spacetimes, uncovering non-commutative structures with compelling properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Spacetimes from General Relativity? Much, Albert General Relativity and Quantum Cosmology Mathematical Physics We introduce a non-commutative product for curved spacetimes, that can be regarded as a generalization of the Rieffel (or Moyal-Weyl) product. This product employs the exponential map and a Poisson tensor, and the deformed product maintains associativity under the condition that the Poisson tensor $Θ$ satisfies $Θ^{μν}\nabla_νΘ^{ρσ}=0$, in relation to a Levi-Cevita connection. We proceed to solve the associativity condition for various physical spacetimes, uncovering non-commutative structures with compelling properties. |
| title | Quantum Spacetimes from General Relativity? |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2404.13029 |