# Do black holes have Arago spots?

I've been reading about Arago spots and the Aragoscope. Some fascinating concepts! Basically, due to wave diffraction, there is a bright spot in the centre of the shadow behind any circular object.

It strikes me that there are some similarities between a black hole and the disc used for the Arago spot experiments. Black holes (or their event horizons) are spherical, so should cast a circular shadow. Have there been any observations of bright spots in the centre of a black hole? If so, would these be useful for astronomy, like a supersized Aragoscope?

I have read that the shadowing object has to be very precisely circular, so I am not sure if a black hole is circular enough. Oblateness caused by rotation might distort the event horizon? There might also be issues with relativity around the fringes of the black hole. I don't have a clear concept of how gravitational lensing and Fresnel diffraction would work together.

A proper analysis of this should treat light as an EM wave propagating in the curved spacetime background of the black hole. The papers

(1) "Wave optics and image formation in gravitational lensing," https://arxiv.org/abs/1207.6846

(2) "Viewing Black Holes by Waves," https://arxiv.org/abs/1303.5520

(3) "Wave Optics in Black Hole Spacetimes: Schwarzschild Case," https://arxiv.org/abs/1502.05468

present analyses for the case of a non-rotating (Schwarzschild) black hole. The papers (1) and (2) use numerical techniques (solving the wave equation for the massless scalar field using a finite difference method) and the paper (3) uses analytic techniques. The abstract of (2) says

We study scattering of waves by black holes. Solving a massless scalar field with a point source in the Schwarzschild spacetime, waves scattered by the black hole is obtained numerically. We then reconstruct images of the black hole from scattered wave data for specified scattering angles. For the forward and the backward directions, obtained wave optical images of black holes show rings that correspond to the black hole glories associated with existence of the unstable circular photon orbit in the Schwarzschild spacetime.

Figure 7 in (2) shows "Images of black holes reconstructed from scattering waves...", and here is an excerpt from that figure:

Notice the relatively bright spot in the center. To help interpret the picture, page 12 says:

In the geometric optics limit, images of black holes can be obtained by solving null geodesics. For the observer at $$\theta_0=0$$, the primary null rays, which are deflected by the black hole but do not go around it, result in the Einstein ring. The secondary and the higher degrees of null rays that go around the black hole many times also form ring images with smaller angular radius compared to the Einstein ring.

This is called the glory effect. The words "Arago spot" are not used in the paper, but the words "Airy disk" are used. The papers (2) and (3) both say that an extension of this analysis to rotating (Kerr) black holes is underway, but I don't know if it has been published yet.

• Great answer, thanks. That image definitely looks similar to an Arago spot, but perhaps a little dimmer. The authors seem to only be commenting on the rings - which are definitely interesting in themselves! This answer triggered me to look up Einstein Rings, and most of the examples had quite a large bright region in the middle. I guess the bright region is the accretion disc, which would hide the Arago spot in most cases? – craq Jan 9 at 3:57
• @craq I would guess that you're right, that something like a bright accretion disk would hide any diffraction-related spot that might otherwise be visible in the center. I didn't find any analyses that accounted for this. – Chiral Anomaly Jan 9 at 4:03
• I think, given today's news release with the first ever photo of a black hole, I have to retract my comment, at least partially. The Einstein Ring photos I was looking at before were lensed by galaxies, and the bright spot in the middle was the galaxy, not the accretion disc. In the new photo, the centre of the black hole actual looks very black, so perhaps the accretion disc wouldn't be a problem for using a black hole as an aragoscope. – craq Apr 10 at 18:59

I also recently learned about Arago spots and had the very same thought regarding black holes. Concerning your retracting part of your comments, it's true that there isn't evidence black boles generally produce Arago spots. That said, while the variables make it unlikely most black holes would produce an Arago spot they also make it likely that a few black holes would produce Arago spots. After all the conditions would have to be perfect (the perfect black holes and the exact pinning up of the light source, the black holes and us, etc.). In the future, after the photographing of thousands of black holes, I wouldn't be surprised if an Arago spot would be among the photographs.