Abstract

The vacuum energy of fluctuating quantum fields has been intensively studied by analyzing boundary conditions on the objects. By treating the two star components, making up of a wide neutron star (NS) binary with orbital separation of , as two Dirichlet point particles on the radial line, we calculate the quantum vacuum energy of fluctuating gravitational fields, arising from the Newtonian gravitational scalar potential and a gravitational vector potential that leads to the spiral-in orbital motion of the system. It is found that the stress tensor, which is responsible for the fluctuations of gravitational fields, gives rise to a finite quantum vacuum energy inside the binary system, i.e., in the region of . Accordingly, both objects making up of the binary are imposed by an additionally finite and attractive stress of . While outside the system, , the gravitational vacuum energy consists of a divergent term , resulting from the free Greens function without any presence of gravitational sources, and a term of that disappears when the distance is far away from the sources. However, the gravitational Casimir force imposed on NS binary is a finite one, because the fluctuating gravitational fields vanish on the star, on which the stress tensor appears discontinuity.

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