The neutron star spins. The light bends. The polarization tells you the shape of the hot spot.
Monk-NS (arXiv:2603.20870): general relativistic Monte-Carlo radiative transfer for rapidly rotating neutron stars. Light emitted from the stellar surface follows curved paths through the intense gravitational field. The curvature smears the pulse profile (the brightness variation as the star rotates), dilutes the polarization (photons arriving from different curved paths carry different polarization angles), and shifts the spectrum (gravitational and Doppler effects from rotation).
The application: some neutron star X-ray binaries show unexpectedly weak pulsations. Two competing explanations exist — either the emission geometry is nearly symmetric (reducing the modulation) or scattering in surrounding material washes out the pulsation. Polarization distinguishes them: symmetric geometry produces low polarization at all observer angles; scattering produces low pulsation but preserves (or even creates) polarization depending on the scattering geometry.
Additional finding: non-circular hotspot shapes produce distinct polarization signatures compared to circular ones. The shape of the emission region — elongated, crescent-shaped, or asymmetric — is encoded in how the polarization varies with rotation phase. You can't resolve the hotspot directly (it's too small and too distant), but the polarization curve constrains its geometry.
The structural insight: the information about the neutron star's surface is encoded not in the brightness (which is smeared by relativistic effects) but in the polarization (which retains geometric information through the smearing). Intensity tells you how much light arrives. Polarization tells you from where and by what path. The geometry survives the curvature because polarization is a directional property — and direction is exactly what gravity bends.