I Appearance of a Kerr black hole from above

[Creedence]

TL;DR Summary

How does it look like?

How does a Kerr black hole look like from above? Is it the same as a Schwarzschild one?
I could not find any convincing visualization for this question.
By above I mean from a point r>0 and ϑ=0.

 

[Dale]

What is the metric for a Kerr black hole and what do you get when you substitute 0 in?

 

[Creedence]

What is the metric for a Kerr black hole and what do you get when you substitute 0 in?

Where to substitute?

 

[Nugatory]

How does a Kerr black hole look like from above? Is it the same as a Schwarzschild one?
I could not find any convincing visualization for this question.
By above I mean from a point r>0 and ϑ=0.

Are you asking for a reasonably technically accurate illustration? That’s what I’m inferring from the word “visualization”.

Of course the black hole itself doesn’t look like much of anything because it neither emits nor reflects light. All the interesting visual effects come from the matter nearby: accretion disks, radiation from infalling matter, jets, ...

 

[Ibix]

One could imagine a large piece of paper with a polar coordinate system drawn on it behind the black hole and ask how the pattern changes as the angular momentum increases, I suppose. Presumably you should hold the irreducible mass constant while doing it, and come up with some way of defining how far away you are in a reasonably consistent manner.

 

[Dale]

Where to substitute?

You said ϑ=0, so substitute 0 into ϑ. It is your scenario, so I don’t know why you asked me that.

 

[A.T.]

Summary: How does it look like?

How does a Kerr black hole look like from above? Is it the same as a Schwarzschild one?
I could not find any convincing visualization for this question.
By above I mean from a point r>0 and ϑ=0.

This is relevant:
https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001
But I don't know if they ever made any visualization looking perpendicular to the plane of rotation.

 

[Creedence]

This is relevant:
https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001
But I don't know if they ever made any visualization looking perpendicular to the plane of rotation.

Yes, this is what bugging me. I've created a simple raytracer some years ago and generated some videos, for example: .
A few weeks ago I started to refactor it and fix its bugs (mostly numerical in the nonlinear computations). For some reasons the black hole is in a fixed position and the rotation axis points to the viewer. The output totally looks like a nonspinning BH. I can't find anything to validate the output.

Edit: The other reason for this question is that the raytracer's old version knew only the Schwarzschild solution. Now I try to add the Kerr solution.

 

[A.T.]

The output totally looks like a nonspinning BH.

What differences did you expect from that view angle?

 

[Creedence]

What differences did you expect from that view angle?

I rendered images of the BH using a square grid background. From that viewpoint the grid may get a vortex-like distortion in the case of a>0. Because of g_tf ≠ 0.

Or with another not so precise wording: the lightrays come from infinity and "parallel" with the rotational axis of the BH get an e_φ speed component. So the image gets a twist in the near of the BH shadow.

 

[A.T.]

I rendered images of the BH using a square grid background.

Try a background that is not scrolling and has better contrast (black lines on white). And increase the spin rate and/or the resolution, in case the effect is still too weak to see.

 

[Ibix]

I would think a better background would be the polar coordinate system I suggested above. I would expect that evenly spaced rings would not appear so, and radial lines would spiral somewhat. One could easily cheat on the rendering in this case by only analysing a single radial line and noting the symmetry. Or maybe a couple of radial lines, to check the symmetry.

 

[A.T.]

One could easily cheat on the rendering in this case by only analysing a single radial line and noting the symmetry. Or maybe a couple of radial lines, to check the symmetry.

@Creedence As Ibix suggests: Before rendering full size videos, one should do some quick tests, to find out what parameters would produce a visible effect. And to verify that the code actually produces that effect at all.

 

[Creedence]

The video I posted is OK. It's generated by my old program version. The actual one generates images with grid background.

Ibix: radial lines is a good idea, thanks.

 

[Creedence]

I would think a better background would be the polar coordinate system I suggested above. I would expect that evenly spaced rings would not appear so, and radial lines would spiral somewhat. One could easily cheat on the rendering in this case by only analysing a single radial line and noting the symmetry. Or maybe a couple of radial lines, to check the symmetry.

The effect is indeed really small, but I could catch it:

 

[A.T.]

The effect is indeed really small, but I could catch it:

Interesting. Is the perceived rotation in two opposite directions just a pattern aliasing effect? Maybe a polar coordinate chart as suggested by @Ibix would indeed be better.

 

[Creedence]

Interesting. Is the perceived rotation in two opposite directions just a pattern aliasing effect? Maybe a polar coordinate chart as suggested by @Ibix would indeed be better.

I think it's anti-aliasing, but I'm not sure. I'll try the polar chart.

 

[A.T.]

I think it's anti-aliasing, but I'm not sure. I'll try the polar chart.

You can see some opposite movement in the simulations by Double Negative:
https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001/data

 

[Creedence]

You can see some opposite movement in the simulations by Double Negative:
https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001/data

Which video are you talking about?

 

[Creedence]

Interesting. Is the perceived rotation in two opposite directions just a pattern aliasing effect? Maybe a polar coordinate chart as suggested by @Ibix would indeed be better.

Rendered a video using a radial pattern in the background:

It is "little" buggy (the ring inside should not be there I think), but the main effect can be seen on it. The spin parameter goes from 0.0 to 2.0 .

 

[A.T.]

It is "little" buggy (the ring inside should not be there I think),

You could check the paths taken by the rays that generate those non-black pixels in that ring, and the black pixels that separate it from the rest.