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Recently, the event horizon of the black hole at the center of M87 was directly imaged by the EHT.

My college professor said this could serve as another test of the accuracy of general relativity. How does the observation test the GR, in detail? And compared with the test of LIGO?

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  • $\begingroup$ GR can explain why the image looks like what you saw in the picture, it explains quantitatively how light emitted by the hot accretion disk that orbits the black hold is bent around the black hole to give you that weird ring around it. Computer simulations of BH using GR produce images that are identical to what you see the real image. The prediction that GR gives to the image is a fine test. LIGO tested other predictions of Einstein’s equations, gravitational waves. Do you want me to expand this explanation with images and intuition or do you feel like you need something more mathematical? $\endgroup$
    – PedroDM
    Commented Aug 3, 2020 at 5:35

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Prior to the EHT images, there were no "zoomed in views" of a black hole candidate.

One of the predictions made by GR is that light travelling in the spacetime metric close to a black hole should follow strongly curved paths. In fact there is a radius, which is a small multiple of the Schwarzschild radius, where if we trace a detected light ray back, it should have arisen after orbiting the black hole one or more times. In contrast, light that came closer to the black hole than this would have fallen in and not escaped. Therefore a clear prediction of GR is that there should be a shadow with a bright ring around it, and the radius of the ring should be a precise multiple of the Schwarzschild radius, given by $2GM/c^2$.

Since, the mass $M$ of the black hole had already been estimated from the observed dynamics of gas orbiting the black hole, there was a reasonably good prediction of the radius of the bright ring.

That the observed radius agrees with this prediction is a test that GR has passed, though it is fair to say it is not a particularly precise test (the error bars are of order 10-20%).

Footnote: The predicted radius (and exact shape) of the ring does depend (at the 10% level) on the spin of the black hole too.

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  • $\begingroup$ Although there is some controversy about whether EHT truly discovered the photon ring: arxiv.org/abs/1906.00873 $\endgroup$
    – Andrew
    Commented Feb 4, 2023 at 21:18
  • $\begingroup$ @Andrew I guess what I don't understand about this and other papers that claim, with simple analytic models, that the EHT got their interpretation wrong, is why a full numerical MHD+GR simulation does produce a bright ring at about $5.2r_s$. If it's just a question of what you call it then fair enough. $\endgroup$
    – ProfRob
    Commented Feb 4, 2023 at 21:47
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My college professor said this could serve as another test of the accuracy of general relativity

Given that GR has already been tested to some ungodly precision, I think the answer is "it can't".

I mean, you can say that it proves that GR is right about BH's, and you could say that's a test of GR, and maybe that's "the accuracy" he's referring to.

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