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), a global submillimeter wavelength very long baseline interferometry array, unveiled event-horizon–scale images of the supermassive black hole M87* as an asymmetric bright emission ring with a diameter of 42 ± 3 μas, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative theories of gravity, while several modified theories of gravity admit non-Kerr black holes. While earlier estimates for the M87* black hole mass, depending on the method used, fall in the range , the EHT data indicated a mass for the M87* black hole of (6.5 ± 0.7) × 10⁹ M _⊙. This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event horizon. The important question arises: Is it possible by a simple technique to estimate black hole parameters from its shadow, for arbitrary models? In this paper, we present observables, expressed in terms of ordinary integrals, characterizing a haphazard shadow shape to estimate the parameters associated with black holes, and then illustrate its relevance to four different models: Kerr, Kerr–Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data.

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb-Ramond field with gravity leads to a power-law hairy black hole having a parameter $s$, which encompasses the Reissner-Nordstrom black hole ($s=1$). We obtain the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb-Ramond black hole, which encompasses, as special cases, Kerr ($s=0$) and Kerr-Newman ($s=1$) black holes. Interestingly, for a set of parameters ($M$, $a$, and $\mathrm{\Gamma }$), there exists an extremal value of the Kalb-Ramond parameter ($s=s_e$), which corresponds to an extremal black hole with degenerate horizons, while for $s<s_e$, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for $s>s_e$. We find that the extremal value $s_e$ is also influenced by these parameters. The black hole shadow size decreases monotonically and the shape gets more distorted with an increasing $s$; in turn, shadows of rotating Kalb-Ramond black holes are smaller and more distorted than the corresponding Kerr black hole shadows. We investigate the effect of the Kalb-Ramond field on the rotating black hole spacetime geometry and analytically deduced corrections to the light deflection angle from the Kerr and Schwarzschild black hole values. The deflection angle for Sgr A* and the shadow caused by the supermassive black hole M87* are included and compared with analogous results of Kerr black holes. The inferred circularity deviation $\mathrm{\Delta }C\le 0.10$ for the M87* black hole merely constrains the Kalb-Ramond field parameter, whereas shadow angular diameter ${\theta }_d=42\pm 3\mu \mathrm{as}$, within the $1\sigma$ region, places bounds $\mathrm{\Gamma }\le 0.09205$ for $s=1$ and $\mathrm{\Gamma }\le 0.02178$ for $s=3$.

We discuss the horizon properties, shadow cast, and the weak gravitational lensing of charged rotating regular black holes, which in addition to mass ($M$) and rotation parameter ($a$) have an electric charge ($Q$) and magnetic charge ($g$). The considered regular black holes are the generalization of the Kerr ($Q=g=0$) and Kerr-Newman ($g=0$) black holes. Interestingly, for a given parameter set, the apparent size of the shadow monotonically decreases and the shadow gets more distorted with increasing charge parameter $Q$. We put constraints on the black hole parameters with the aid of recent M87* shadow observation. The conserved quantities associated with the rotating regular black holes are calculated and also a brief description of the weak gravitational lensing using the Gauss-Bonnet theorem is presented. Interestingly, the deflection angle decreases with the charge of the black hole. Our results vis-à-vis go over to the Kerr and Kerr-Newman black holes in the appropriate limits.