# Frame-dragging effects in obliquely rotating magnetars

## TL;DR

This paper investigates how frame-dragging effects in obliquely rotating magnetars influence particle orbits, gravitational wave emission, and energy loss, highlighting the dependence on magnetic field strength and misalignment angle.

## Contribution

It provides a relativistic analysis of frame-dragging in oblique magnetars, revealing its impact on particle trajectories and gravitational wave signals, which was not previously detailed.

## Key findings

- Polar frame-dragging causes non-planar particle orbits.
- Gravitational wave amplitude depends on misalignment angle and frame-dragging velocities.
- Energy loss is significantly affected by polar frame-dragging velocity.

## Abstract

Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodesic of a particle near the star's surface. The polar frame-dragging velocity makes the particle orbit non-planar, and the particle moves both along the azimuthal and polar direction for a fixed radial distance. The extent of particle deviation from planar orbit depends on the magnetic field strength and the misalignment angle. We find that the continuous gravitational wave emitted from such obliquely rotating axisymmetric star is non zero, and for small misalignment angle, the gravitational wave amplitude depends more on the azimuthal frame-dragging velocity. In contrast, for a large misalignment angle, the polar frame-dragging velocity dominates. The energy loss from such a misaligned rotator depends more significantly on the polar frame-dragging velocity and therefore, can significantly affect the magnetosphere around a magnetar.