A cinematographer filming a black hole faces a fundamental problem: light from different parts of the accretion disk reaches the camera at different times. The near edge flares up today, the far edge a week ago, and the jet trails months behind. If you splice all the frames without paying attention to age, you get not a movie but a collage of pieces from different times.
A full account of the finite speed of light requires holding hundreds of three-dimensional plasma snapshots in memory at once. For one M87* model, that is 903 layers occupying 65 gigabytes, too much for a typical workstation. Fast approximations read the same snapshot for all rays, but they break down on extended jets and polarization, where Faraday effects rotate the plane of light oscillation even in regions where the light itself is barely emitted.
The new method CoportSL acts like an experienced editor who first reviews all the footage on fast forward. For each region of space, it estimates the contribution to emission, absorption, and Faraday effects, and then it keeps the time dependence only where the total contribution exceeds a given threshold. Elsewhere, time is frozen, but radiative transfer is still computed along the entire ray. Additionally, the method constructs an effective time window from the distribution of delays within the selected region, discarding rare tails, just as an editor throws out random frames that do not affect the plot.
In tests with a magnetically arrested disk similar to M87*, the method reduced the number of simultaneously loaded layers from 903 to 223 for the region near the horizon and from 897 to 496 for the jet. The maximum error in polarization images did not exceed 4 thousandths compared to the full calculation. Memory usage dropped from 65.7 to 20.2 gigabytes for the near image and from 64.1 to 37.3 gigabytes for the jet, which fits on a workstation. The computation time per frame with the hybrid slow method remained comparable to the fast method at low core counts and only 1.9 times longer on 64 cores.
The editor returns to the film, now knowing which scenes must not be touched. Fast and slow light curves nearly coincide near the horizon, but for the jet, a global time shift does not eliminate local discrepancies, and spatial differences in polarization remain significant. This means that neglecting the finite speed of light can lead to incorrect interpretation of the magnetic structure near the horizon. The method can already be applied to prepare libraries of synthetic images and light curves for comparison with observations from the Event Horizon Telescope and the future ngEHT.
For M87*, one gravitational radius is about 9.6 billion kilometers, and the time for light to cross it is roughly 8.9 hours. In the paper, delays are measured in these units, and even a 'short' window of 110 gravitational radii means a spread in emission times of almost 41 days.
In the movie 'Interstellar', time delay near the black hole Gargantua is shown as gravitational time dilation, but here it is different: light from different parts of the disk reaches the camera at different times, and without accounting for this, the image would not just be shifted but assembled from pieces of different ages, like a collage.