Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical general relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A ∗ (Sgr A ∗ ), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A ∗ ’s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A ∗ places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A ∗ and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well-motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.

The Event Horizon Telescope (EHT) collaboration has recently released the first image of a black hole (BH), opening a new window onto tests of general relativity in the strong field regime. In this paper, we derive constraints on the nature of M87* (the supermassive object at the center of the galaxy M87), exploiting the fact that its shadow appears to be highly circular, and using measurements of its angular size. We first consider the simple case where M87* is assumed to be a Kerr BH. We find that the inferred circularity of M87* excludes Kerr BHs with observation angle ${\theta }_{\mathrm{obs}}\gtrsim 45°$ for dimensionless rotational parameter $0.95\lesssim a_{*}\le 1$ whereas the observation angle is unbounded for $a_{*}\lesssim 0.9$. We then consider the possibility that M87* might be a superspinar, i.e., an object described by the Kerr solution and spinning so fast that it violates the Kerr bound by having $|a_{*}|>1$. We find that, within certain regions of parameter space, the inferred circularity and size of the shadow of M87* do not exclude the possibility that this object might be a superspinar.

Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity, but there is not yet direct observational evidence that the spacetime geometry around these objects is described by the Kerr solution. The study of the properties of the electromagnetic radiation emitted by gas or stars orbiting these objects can potentially test the Kerr black hole hypothesis. This paper reviews the state of the art of this research field, describing the possible approaches to test the Kerr metric with current and future observational facilities and discussing current constraints.

We consider the possibility that astrophysical black holes (BHs) can violate the Kerr bound; i.e., they can have angular momentum greater than BH mass, $J>M$. We discuss implications on the BH apparent shape. Even if the bound is violated by a small amount, the shadow cast by the BH changes significantly (it is $\sim$ an order of magnitude smaller) from the case with $J\le M$ and can be used as a clear observational signature in the search for super-spinning BHs. We discuss briefly recent observations in the mm range of the supermassive BH at the center of the Galaxy, speculating on the possibility that it might violate the Kerr bound.