IS GRAVITATIONAL VACUUM ENERGY RENORMALIZEDIN NEUTRON STAR BINARY?

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.