Gravitationally Induced Polarization-Angle Rotation in Pulsar-Black Hole Binaries

Radio pulsars emit highly polarized radiation whose polarization properties are commonly described by the Rotating Vector Model (RVM). In this work, we investigate the effects of gravitational light bending and parallel transport on the polarization profile of a pulsar in a hypothetical binary system with a black hole (BH) companion. We combine the RVM with numerical integration of null geodesics to calculate the polarization direction along the photon trajectory and model the orbital-phase-dependent variation of the observed polarization position angle (PPA). We consider both non-spinning and spinning black hole companions and include the evolution of the orbital geometry due to relativistic spin-orbit coupling. For a non-spinning black hole, the change in the observed polarization direction arises from the geometric shift associated with gravitational light bending. For a spinning black hole, frame dragging introduces an additional geometric shift, while parallel transport produces an additional polarization rotation measured relative to our chosen reference construction. We investigate the dependence of these polarization changes on the binary parameters and the orientation of the pulsar spin. We find that gravitational light bending can significantly distort the characteristic S-shaped PPA profile, particularly near superior conjunction, and can reverse its overall sense of variation for the supermassive black hole system considered here. Relativistic spin-orbit evolution also affects the orbital-phase dependence of the polarization profile, particularly in the supermassive black hole system. These results show that relativistic photon propagation can modify both the shape and the phase dependence of pulsar polarization profiles and may provide a useful probe of the geometry of pulsar-BH binaries when such systems are discovered.