Vacuum and plasma magnetosphere around rotating magnetized neutron stars in Bocharova–Bronnikov–Melnikov–Bekenstein geometry

In this work, we explore the vacuum and plasma magnetosphere of a slowly rotating, magnetized neutron star in a conformally coupled scalar field, so-called Bocharova–Bronnikov-Melnikov–Bekenstein (BBMB) geometry. Starting from the vacuum solutions to Maxwell’s equations in a curved spacetime, we derive modified magnetic and electric field structures in the BBMB geometry. We then investigate the behavior of the Goldreich–Julian (GJ) charge density, accelerating electric fields parallel to magnetic field lines, pair production thresholds, and the rate of energy loss through dipolar radiation in the magnetized star. The coupled scalar field significantly enhances magnetic field strength, charge separation, and parallel acceleration, as well as particle acceleration. We also study the deathline conditions that are responsible for secondary pair formation in the BBMB geometry. All results are compared with the general relativistic (GR) limit. As a result, deathline in the P-P˙ diagram is located above in the spacetime compared with GR frame, implying extended pulsar activity compared to GR. Radiative luminosities from the magnetodipolar radiation process are also increased compared to GR predictions. These findings suggest that BBMB gravity could play a crucial role in shaping the high-energy phenomena of neutron stars and offer new avenues for testing gravity in strong-field regimes.