Forward Ray Tracing and Hot Spots in Kerr Spacetime

TL;DR

This paper introduces an efficient forward ray tracing method for Kerr spacetime that accurately models hotspots near black holes, capturing multiple images and aiding in spacetime tomography and black hole parameter estimation.

Contribution

We develop a novel analytic integral-based Kerr geodesic ray tracing technique that improves modeling accuracy and computational efficiency for black hole hotspot imaging.

Findings

Enhanced identification of strongly lensed photons

Improved accuracy in hotspot shape and amplification modeling

Facilitates black hole spacetime tomography

Abstract

Hotspots, often characterized as pointlike emissions, frequently appear near black holes with significantly enhanced luminosity compared to the surrounding accretion flow. Notably, such hotspots are regularly observed near the black hole at the center of the Milky Way. Light rays emitted from these sources follow complex trajectories around the black hole before reaching distinct locations on the observer's image plane. Precisely resolving both direct emissions and their higher-order images--despite the latter's intensity suppression--is essential for extracting detailed spacetime information, including the black hole's mass, spin, and inclination angle. To improve the accuracy and efficiency of hotspot modeling, we develop a forward ray tracing method based on the analytic integral solution of Kerr geodesics, leveraging conserved quantities. Our approach traces geodesics from a given emission point near the black hole to a distant observer, effectively capturing multiple images with a tailored parametrization scheme for root-finding. By perturbing these geodesics, we map finite-size emissions to distinct regions on the image plane, enabling the quantification of image shapes and amplification rates. This method not only enhances the identification of strongly lensed photons from black holes but also enables efficient spacetime tomography and hotspot localization, leveraging observations from the Event Horizon Telescope and its upcoming next-generation upgrades.