General Relativity and Gravitation, Vol. 30, No. 6, 1998 Gravitational EŒects on the Vortex Distribution in Relativistic Super¯uid Stars H. Casini 1 and R. Montemayor 1,2 Received August 5, 1997. Rev. version March 9, 1998 Neutron stars are supposed to be mainly formed by a neutron super¯uid. The angular momentum is given by the vortex array within the ¯uid, and a good account of the observable eŒects is determined by its cou- pling with the crust. In this article we show that the gravitational ®eld introduces important modi®cations in the vortex distribution and shape. The inertial frame dragging on the quantum ¯uid produces a decrease in the vortex density, which for realistic models is in the order of 15%. This eŒect is relevant for neutron star rotation models and can provide a good framework for checking the quantum eŒect of the frame dragging. KEY WORDS : Frame dragging ; neutron stars ; super¯uid vortices 1. INTRODUCTION In most quantum systems the gravitational eŒects are extremely small, but there are some remarkable exceptions. One which has been already extensively studied is the generation of inhomogeneities in the in¯ation- ary phase of the universe, through the ampli®cation and the transition to a classical regime of the quantum ¯uctuation of the in¯aton ®eld [1]. In this case the relevance of the phenomena is related to the propagation of modes with a wavelength comparable to the radius of the horizon of the universe, i.e., the gravitational and the quantum characteristic lengths are of the same order. A natural question which arises is whether there 1 Instituto Balseiro and Centro At  omico Bariloche, Universidad Nacional de Cuyo and CNEA, 8400 S.C. de Bariloche, R õo Negro, Argentina 2 E-mail: montemay@cab.cnea.edu.ar 849 0001-7701/ 98/ 0600-0849$15.00/ 0 1998 Plenum Publishing Corporation