Note on the local calculation of decoherence of quantum superposition in the static black holes

Abstract:We investigate the decoherence of a quantum spatial superposition of a static particle in Schwarzschild and Reissner-Nordström black holes. By treating the particle as a localized classical source coupled to a quantum scalar field, we reformulate the decoherence process in the Danielson-Satishchandran-Wald (DSW) gedankenexperiment through coherent state generation and derive the local expression for the decoherence functional in terms of the Wightman function. In the long-time limit, the decoherence rate is shown to be characterized by the low-frequency behavior of the Wightman function. We then employ the asymptotic matching method to calculate the analytical expressions of the Wightman functions in the Boulware, Unruh, and Hartle-Hawking vacua. We show that the decoherence behavior depends on the quantum state of the environmental field. While the Boulware vacuum gives vanishing decoherence for a static superposition, the thermal effects associated with Hawking radiation in the Unruh and Hartle-Hawking vacua can induce nonvanishing decoherence.

arXiv:2606.14178 [gr-qc]

(or arXiv:2606.14178v1 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2606.14178 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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