# Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole

## TL;DR

This paper studies the complex spin and orbital dynamics of a millisecond pulsar orbiting a massive black hole, highlighting observable effects like precession and nutation that can be detected through pulsar timing and gravitational wave observations.

## Contribution

It applies the MPD formulation to model spin-orbit and spin-curvature interactions in pulsar-black hole binaries, revealing non-planar orbits and observable signatures.

## Key findings

- MSP spin exhibits precession and nutation due to spin-orbit coupling.
- Orbital motion is non-planar and deviates from Keplerian orbits.
- Observable signatures include variations in pulsar emission and self-occultation.

## Abstract

We investigate the spin dynamics of a millisecond pulsar (MSP) in a tightly bounded orbit around a massive black hole. These binaries are progenitors of the extreme-mass-ratio-inspirals (EMRIs) and intermediate-mass-ratio-inspirals (IMRIs) gravitational wave events. The Mathisson-Papapetrou-Dixon (MPD) formulation is used to determine the orbital motion and spin modulation and evolution. We show that the MSP will not be confined in a planar Keplerian orbit and its spin will exhibit precession and nutation induced by spin-orbit coupling and spin-curvature interaction. These spin and orbital behaviours will manifest observationally in the temporal variations in the MSP's pulsed emission and, with certain geometries, in the self-occultation of the pulsar's emitting poles. Radio pulsar timing observations will be able to detect such signatures. These extreme-mass-ratio binaries (EMRBs) and intermediate-mass-ratio binaries (IMRBs) are also strong gravitational wave sources. Combining radio pulsar timing and gravitational wave observations will allow us to determine the dynamics of these systems in high precision and hence the subtle behaviours of spinning masses in strong gravity.