Light Propagation Prescriptions for Black Hole Movies

TL;DR

This paper compares different light propagation models in black hole imaging, introducing an intermediate 'brisk light' approach that better captures temporal effects relevant for future observations.

Contribution

It introduces the 'brisk light' prescription, an efficient method to incorporate lensing delay structures in black hole movies, bridging slow and fast light models.

Findings

High-inclination mismatch can reach tens of percent when variability timescale is short.

The 'brisk light' method effectively captures dominant temporal features of lensing delays.

The methodology aids in understanding when slow light effects are significant for black hole imaging.

Abstract

The spatiotemporal content of a black-hole movie is set jointly by source variability and by the distribution of light-travel times across the image. In the slow-light prescription, an image evaluated at fixed observer time contains photons emitted at different source times, whereas in fast light all rays sample a single source emission time. In this work we compare these light-propagation prescriptions through the lensing-band structure of Kerr geodesic delays in a controlled semi-analytic setting. For a given emitting geometry, black-hole spin, and observer inclination, we show how the coordinate-time delay distributions of Kerr null geodesics, decomposed by image order across lensing bands, can be compared with the source correlation time to quantify differences between light-propagation prescriptions. We find that when the intrinsic variability timescale is comparable to, or shorter than, the relevant delay spread, the high-inclination mismatch between fast- and slow-light curves can reach several tens of percent. Motivated by this geometric structure, we introduce brisk light, an intermediate prescription that compresses each lensing-band delay map to its dominant temporal interval rather than collapsing the full image to a single source time. The proposed methodology provides both a practical criterion for when slow light matters and an efficient route to black-hole movies that retain the leading temporal imprint of strong lensing, a regime of direct relevance for future space-based VLBI targeting photon-ring observables.