Self-gravitating Schrödinger--Poisson Solitons in Curved Spacetime

We formulate a description of self-gravitating Schrödinger--Poisson (SP) solitons in curved spacetime using a local inertial frame centered on the soliton. In the weak-field and non-relativistic regime, the effect of the background spacetime is incorporated into the SP equations through an effective tidal potential determined by the spacetime curvature. We apply this framework to a soliton moving along a circular equatorial geodesic around a Kerr black hole. The tidal field contains stationary and time-dependent quadrupolar components, which induce a deformation of the soliton and an associated mass quadrupole moment. We formulate the quadrupolar response in terms of the tidal deformability and the dimensionless Love number. We then estimate the gravitational radiation associated with the rotating deformed soliton and evaluate the corresponding characteristic strain for representative soliton sizes and orbital radii. A comparison with representative sensitivity curves of planned space-based gravitational-wave detectors identifies parameter regimes in which the estimated characteristic strain may lie within their sensitivity ranges. Our framework provides a systematic basis for investigating the tidal response of self-gravitating bosonic solitons in black-hole spacetimes and their potential gravitational-wave signatures.