Polarization Patterns of the Hotspots Plunging into a Kerr Black Hole

The multi-wavelength polarized light signals from supermassive black holes have sparked many studies on polarized images of accretion disks and hotspots. However, the polarization patterns within the innermost stable circular orbit (ISCO) region remain to be explored. In this study, we focus on two specific types of orbits, namely the plunging geodesics inward from the ISCO and homoclinic geodesics, to uncover the polarization features associated with non-circular motion in a Kerr spacetime. For an on-axis observer, we specifically develop an approximate function to describe gravitational lensing along the azimuthal direction and establish a simplified synchrotron emission model. Based on these, we analyze the time-integrated polarized images of hotspots and their Stokes parameters. Moreover, we explore the polarized image of the plunging region within a thin accretion disk.