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Gravitational Casimir Effect in Inspiralling Neutron Star Binary

Currently, the discussions and investigations for the vacuum energy is drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e. the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwinger's source theory and study the Casimir effect due to the quantization of gravitation, i.e. the gravitational Casimir effect (GCE), in inspiraling neutron star (NS) binaries with wide separation of $10^9 \rm m$. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the contributions of GEM to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the orbital separation of the binary decay a distance of $L$ in radial direction, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition the gravitational force. The gravitational waves (GWs), emitted from wide inspiraling NS binaries, locate in the low-frequency band of $10^{-4}-1$ Hz. For a characteristic GW frequency of $10^{-3}$ Hz, the gravitational Casimir correction to the signals is estimated as of the order of $\sim10^{-24}$, which corresponds to a force of $10^{-20}$ N. By considering that the sensitivity of space-based gravitational wave observatory, LISA/eLISA and Taiji, can be reduced to $10^{-24}$, we would expect that LISA/eLISA and Taiji with sensitivity improvements give the powerful tool to detect GCE in the near future.