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.

We study the shadows cast by the different types of rotating regular black holes viz. Ayón-Beato-García (ABG), Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$). Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically, and the distortion parameter increases when the values of these parameters increase. A comparison with the standard Kerr case is also investigated. We have also studied the influence of the plasma environment around regular black holes to discuss its shadow. The presence of the plasma affects the apparent size of the regular black hole’s shadow to be increased due to two effects: (i) gravitational redshift of the photons and (ii) radial dependence of plasma density.

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study the shadow cast by the five-dimensional Myers-Perry black hole with equal rotation parameters. We demonstrate that the null geodesic equation can be integrated, which provides us an opportunity to investigate the shadow cast by a black hole. The shadow of a black hole is found to be a dark zone covered by a deformed circle. Interestingly, the shapes of the black hole shadow are more distorted and the size decreases for larger black hole spins. Interestingly, it turns out that, for fixed values of the rotation parameter, the shadow is slightly smaller and less deformed than for its four-dimensional Kerr black hole counterpart. Further, the shadow of the five-dimensional Kerr black hole is concentric deformed circles. The effect of the rotation parameter on the shape and size of a naked singularity shadow is also analyzed.

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.

It is believed that curvature singularities are a creation of general relativity and, hence, in the absence of a quantum gravity, models of nonsingular black holes have received significant attention. We study the shadow (apparent shape), an optical appearance because of its strong gravitational field, cast by a nonsingular black hole which is characterized by three parameters, i.e., mass ($M$), spin ($a$), and a deviation parameter ($k$). The nonsingular black hole under consideration is a generalization of the Kerr black hole that can be recognized asymptotically ($r\gg k,k>0$) explicitly as the Kerr-Newman black hole, and in the limit $k\to 0$ as the Kerr black hole. It turns out that the shadow of a nonsingular black hole is a dark zone covered by a deformed circle. Interestingly, it is seen that the shadow of a black hole is affected due to the parameter $k$. Indeed, for a given $a$, the size of a shadow reduces as the parameter $k$ increases, and the shadow becomes more distorted as we increase the value of the parameter $k$ when compared with the analogous Kerr black hole shadow. We also investigate, in detail, how the ergoregion of a black hole is changed due to the deviation parameter $k$.