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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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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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