Testing modified gravity with black hole shadows

Black hole shadow in the movie “Interstellar.” Image credit: Double Negative artists/DNGR/TM © Warner Bros. Entertainment Inc./Creative Commons (CC BY-NC-ND 3.0) license.

On my visit to Perimeter Institute last week, I talked to John Moffat, whose recent book “Cracking the Particle Code of the Universe” I much enjoyed reading. Talking to John is always insightful. He knows the ins and outs of both particle physics and cosmology, has an opinion on everything, and gives you a complete historical account with this. I have learned a lot from John, especially to put today’s community squabbles into a larger perspective.

John has dedicated much of his research to alternatives to the Standard Model and the cosmological Concordance Model. You might mistake him for being radical or having a chronical want of being controversial, but I assure you neither is the case. The interesting thing about his models is that they are, on the very contrary, deeply conservative. He’s fighting the standard with the standard weapons. Much of his work goes largely ignored by the community for no particular reason other than that the question what counts as an elegant model is arguably subjective. John is presently maybe best known for being one of the few defenders for modified gravity as an alternative to dark matter made of particles.

His modified gravity (MOG) that he has been working on since 2005 is a covariant version of the more widely known MOdified Newtonian Dynamics (or MOND for short). It differs from Bekenstein’s Tensor-Vector-Scalar (TeVeS) model in the field composition; it also adds a vector field to general relativity but then there are additional scalar fields and potentials for the fields. John and his collaborators claim they can fit all the evidence for dark matter with that model, including rotation curves, the acoustic peaks in the cosmic microwave background and the bullet cluster.

I can understand that nobody really liked MOND which didn’t really fit together with general relativity and was based on little more than the peculiar observation that galaxy rotation curves seem to deviate from the Newtonian prediction at a certain acceleration rather than at a certain radius. And TeVeS eventually necessitated the introduction of other types of dark matter, which made it somewhat pointless. I like dark matter because it’s a simple solution and also because I don’t really see any good reason why all matter should couple to photons. But I do have some sympathy for modifying general relativity, though, having tried and failed to do it consistently has made me vary of the many pitfalls. For what MOG is concerned, I don’t see a priori why it’s worse adding a vector field and some scalar fields than adding a bunch of other fields for which we have no direct evidence and then giving them names like WIMPS or axions.

Quite possibly the main reason MOG isn’t getting all that much attention is that it’s arguably unexciting because, if correct, it just means that none of the currently running dark matter experiments will detect anything. What you really want is a prediction for something that can be seen rather than a prediction that nothing can be seen.

That’s why I find John’s recent paper about MOG very interesting, because he points out an observable consequence of his model that could soon be tested:

Modified Gravity Black Holes and their Observable Shadows
J. W. Moffat
European Physics Journal C (2015) 75:130
arXiv:1502.01677 [gr-qc]

In this paper, he has studied how black holes in this modification of gravity differ from ordinary general relativity, and in particular calculated the size of the black hole shadow. As you might have learned from the movie “Interstellar,” black holes appear like dark disks surrounded by rings that are basically extreme lensing effects. The size of the disk in MOG depends on a parameter in the model that can be determined from fitting the galaxy rotation curves. Using this parameter, it turns out the black hole shadow should appear larger by a factor of about ten in MOG as compared to general relativity.

So far nobody has seen a black hole shadow other than in the movies, but the Event Horizon Telescope will soon be looking for exactly that. It isn’t so much a telescope but a collaboration of many telescopes all over the globe, which allows for a very long baseline interferometry with unprecedented precision. In principle they should be able to see the shadow.

What I don’t know though is whether the precision of both radius of the shadow and the mass will be sufficient to make a distinction between normal and modified general relativity in such an experiment. I am also not really sure that the black hole solution in the paper is really the most general solution one can obtain in this type of model, or if not there is some way to backpedal to another solution if the data doesn’t fulfill hopes. And then the paper contains the somewhat ominous remark that the used value for the deviation parameter might not be applicable for the black holes the Event Horizon Telescope has set its eyes on. So there are some good reasons to be skeptic of this and as the scientists always say “more work is needed.” Be that as it may, if the event horizon telescope does see a shadow larger than expected, then this would clearly be a very strong case for modified gravity.