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Quantum Spacetimes from General Relativity?

Published 19 Apr 2024 in gr-qc, math-ph, and math.MP | (2404.13029v1)

Abstract: 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 $\Theta$ satisfies $\Theta{\mu\nu}\nabla_{\nu}\Theta{\rho\sigma}=0$, 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.

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