Pulsar magnetospheres in dynamical Chern-Simons gravity: deathline conditions and polar-cap particle acceleration
The role of surface gravity in neutron stars (NSs) is considerable in the radiation mechanisms of the surrounding plasma magnetosphere near the star surface, as they are highly magnetized, compact gravitating objects with compactness $M/R \simeq 0.2$. In this context, they serve as a celestial laboratory for testing gravity theories that dominate the stars' exteriors through plasma magnetospheric radiation. In this paper, we examine how dynamical Chern-Simons (dCS) gravity modifies pulsar electrodynamics in the slow-rotation, weak-coupling regime; the leading-order correction affects only the off-diagonal metric component $g_{tϕ}$, while the diagonal components remain as in General Relativity (GR). We first solve the Maxwell equations in the dCS framework for the electromagnetic field components and obtain analytical solutions for the electric and magnetic fields. We show that the magnetic field components are the same as in GR, while the electric field components are modified in dCS. We then derive analytic expressions for the induced electric charge density, known as the Goldreich-Julian (GJ) charge density, which sources the induced electric field arising from the magnetic field and the star's rotation. In dCS, it is larger than in the GR case, whereas the accelerating electric field parallel to the magnetic field lines is weaker. Next, we consider the deathline condition for switching off electron and positron radiation via inverse Compton scattering in the star's polar cap zone and show that the line shifts upward in the $P-\dot{P}$ diagram, explaining the physics of shorter-lived pulsars. Lastly, we study charged-particle acceleration in the polar cap region and show that electrons reach higher energies over shorter distances than in the GR case.