We investigate the dynamic Casimir effect (DCE) of a ($1+1$)-dimensional free massless scalar field in a finite or semi-infinite cavity for which the boundary condition (BC) instantaneously changes from the Neumann to the Dirichlet BC or reversely. While this setup is motivated by the gravitational phenomena, such as the formation of strong naked singularities or wormholes, and the topology change of spacetimes or strings in quantum gravity, the analysis is quite general. For the Neumann-to-Dirichlet cases, we find two components of diverging flux emanate from the point where the BC changes. We carefully compare this result with that of Ishibashi and Hosoya (2002) obtained in the context of a quantum version of cosmic censorship hypothesis, and show that one of the diverging components was overlooked by them and is actually nonrenormalizable, suggesting to bring non-negligible backreaction or semiclassical instability. On the other hand, for the Dirichlet-to-Neumann cases, we reveal for the first time that only one component of diverging flux emanates, which is the same kind as that overlooked in the Neumann-to-Dirichlet cases. This result suggests not only the robustness of the appearance of diverging flux in instantaneous limits of DCE but also that the type of divergence sensitively depends on the combination of initial and final BCs.

• Received 31 October 2018
• Revised 24 December 2018

DOI:https://doi.org/10.1103/PhysRevD.99.025012

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Published by the American Physical Society