Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lines by brane tension. The implication of this effect to the magnetospheric energy loss problem is underlined. It was found that for initially zero potential and field on the surface of a neutron star, the amplitude of the plasma mode created by Goldreich-Julian charge density will increase in the presence of the negative brane charge. Finally we derive the equations of motion of test particles in magnetosphere of slowly rotating star in the braneworld. Then we analyze particle motion in the polar cap and show that brane tension can significantly change conditions for particle acceleration in the polar cap region of the neutron star.

The phase shift a neutron interferometer caused by the gravitational field and the rotation of the earth is derived in a unified way from the standpoint of general relativity. General relativistic quantum interference effects in the slowly rotating braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-time. In the case of neutron interferometry it is found that due to the presence of the parameter Q * an additional term in the phase shift of interfering particle emerges from the results of the recent experiments we have obtained upper limit for the tidal charge as Q * 10 7 cm 2 . Finally, as an example, we apply the obtained results to the calculation of the (ultra-cold neutrons) energy level modification in the braneworld.

The paper explores the thermodynamic properties of primordial black holes (PBHs) in the braneworld. Specifically, the researchers examined Hawking radiation and the lifetime of PBHs. Through their analysis, an exact analytical expression for the Bekenstein–Hawking entropy, temperature, and heat capacity was derived. Their findings suggest that the lifetime of PBHs in the early universe is reduced by at least one order of magnitude, ultimately leading to their evaporation. This could explain why we have not observed the final rapid evaporation of PBHs in the recent epoch of the universe.