[aplavin]

One side of the accretion disk is indeed brighter than the other – in the default view in the app, the bottom part is brighter. The effect appears quite clearly visible to me, although the exact contrast depends on the colorscale mapping. Here, I tried to find a colorscale that works well for both the disk and the jet, which naturally means the leading/trailing edge contrast can be less than in the linear mapping. Hope it explains the visual effect!

Kerr vs Schwarzschild (static vs rotating black holes) is a much smaller effect visually – that's why it is so hard for us to measure black hole spins (= how fast they are rotating) observationally, even with the Event Horizon Telescope.

[csmoak]

I think the contrast between the two sides is typically greater with an optically thick disk, and it looks like you are rendering an optically thin disk. I think that's the main difference from what I was expecting when I saw it.

Very cool demo! Thanks for sharing!

(For reference, my experience rendering black holes is recreating Luminet's rendering from the late 70s: https://www.ioccc.org/2025/cesmoak/index.html )

[aplavin]

True, the disk is rendered optically (and geometrically) thin. This is done so that real-time performance is attained on devices like phones – volumetric GR rendering would be significantly more expensive. The jet (zoom out to see it) is rendered with full volumetric effects, because it's just special relativity there.

Fortran punchcard style to render black holes?! That's really going full circle to the origins, I really enjoyed reading about Luminet's work some time ago.

[csmoak]

Oh nice, I had not zoomed out enough. I don't think I've seen the relativistic jets rendered before. The AR mode looks great on my phone.

Yep, I had fun learning a lot about punchcards, Fortran, and the math behind black holes. I suspect I'm doing something similar to you in my Fortran implementation, raymarching along the null geodesic to come up with my final image: https://imgur.com/a/czysDls

Also, I have to point out the "going full circle" pun, intended or not.

[aplavin]

Actually, the jet was the first part of the app – I wanted to just see and "feel" relativistic beaming in practice, in physical space. And it was fun and instructive indeed! Really puts into perspective how tight is the jet vs line-of-sight alignment for those bright jets we see across the universe. And how beaming is the dominant effect that determines the jet/quasar appearance.

[csmoak]

I guess the fact we see any at all given the distance and small angles just emphasizes how many there are out there...

[aplavin]

Yes, even observing a single jet pointed towards us (typically, at just a few degrees) is routinely used a strong argument for existence of many similar powerful sources, just misaligned with the Earth. Arguments like:

- See a jet at redshift z ~ 6? There are thousands more!

- See that well-aligned blazar jets are among strongest gamma ray (or neutrino) sources? Gamma rays/neutrinos are preferentially emitted along the jet direction, otherwise we'd seen thousands more equally strong sources.