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.

In this study, we found a new traversable wormhole solution in the framework of a bumblebee gravity model. With these types of models, the Lorentz symmetry violation arises from the dynamics of a bumblebee vector field that is nonminimally coupled with gravity. To this end, we checked the wormhole’s flare-out and energy (null, weak, and strong) conditions. We then studied the deflection angle of light in the weak limit approximation using the Gibbons-Werner method. In particular, we show that the bumblebee gravity effect leads to a nontrivial global topology of the wormhole spacetime. By using the Gauss-Bonnet theorem (GBT), it is shown that the obtained non-asymptotically flat wormhole solution yields a topological term in the deflection angle of light. This term is proportional to the coupling constant, but independent from the impact factor parameter. Significantly, we showed that the bumblebee wormhole solutions, under specific conditions, support the normal matter wormhole geometries.

In this paper the deflection angle of light by a rotating Teo wormhole spacetime is calculated in the weak limit approximation. We mainly focus on the weak deflection angle by revealing the gravitational lensing as a partially global topological effect. We apply the Gauss-Bonnet theorem (GBT) to the optical geometry osculating the Teo-Randers wormhole optical geometry to calculate the deflection angle. Furthermore we find the same result using the standard geodesic method. We have found that the deflection angle can be written as a sum of two terms, namely the first term is proportional to the throat of the wormhole and depends entirely on the geometry, while the second term is proportional to the spin angular momentum parameter of the wormhole. A direct observation using lensing can shed light and potentially test the nature of rotating wormholes by comparing with the black holes systems.

The presence of dark matter around a black hole remarkably affects its spacetime. We consider the effects of dark matter on the shadow of a new solution to the Einstein equations that describes a rotating black hole in the background of perfect dark matter fluid, along with its extension to nonzero cosmological constant $\mathrm{\Lambda }$. Working in Boyer-Lindquist coordinates, we consider the effects of the perfect dark matter fluid parameter $\alpha$ on the shadow cast by a black hole with respect to an observer at position $(r_o,{\theta }_o)$. By applying the Gauss-Bonnet theorem to the optical geometry, we find that notable distortions from a Kerr black hole can occur. We describe their dependence on $\alpha$ and $\mathrm{\Lambda }$.

In this paper we present a new black hole solution surrounded by dark matter (DM) halo in the galactic center using the mass model of M87 and that coming from the universal rotation curve (URC) dark matter profile representing family of spiral galaxies. In both cases the DM halo density is cored with a size $r_0$ and a central density ${\rho }_0$: $\rho (r)={\rho }_0/(1+r/r_0)(1+(r/r_0{)}^2)$. Since $r_0{\rho }_0=120{\mathrm{M}}_{\odot }/{\mathrm{pc}}^2$ [ Mon. Not. R. Astron. Soc. 397, 1169 (2009)], then by varying the central density one can reproduce the DM profile in any spiral. Using the Newman-Jains method we extend our solution to obtain a rotating black hole surrounded by dark matter halo. We find that the apparent shape of the shadow beside the black hole spin $a$, it also depends on the central density of the surrounded dark matter ${\rho }_0$. As a specific example we consider the galaxy M87, with a central density ${\rho }_0=6.9\times {10}^6{\mathrm{M}}_{\odot }/{\mathrm{kpc}}^3$ and a core radius $r_0=91.2\mathrm{kpc}$. In the case of M87, our analyses show that the effect of dark matter on the size of the black hole shadow is almost negligible compared to the shadow size of the Kerr vacuum solution hence the angular diameter $42\mu \mathrm{as}$ remains almost unaltered when the dark matter is considered. For a small totally dark matter dominated spiral such as UGC 7232, we find similar effect of dark matter on the shadow images compared to the M87. However, in specific conditions having a core radius comparable to the black hole mass and dark matter with very high density, we show that the shadow images decreases compared to the Kerr vacuum black hole. The effect of dark matter on the apparent shadow shape can shed some light in future observations as an indirect way to detect dark matter using the shadow images.

In this paper, we study the shadow cast by two types of charged and slowly rotating black holes in the Einstein-Æther theory of gravity. These two types of black holes correspond to two specific combinations of the coupling constants of the æther field, i.e., $c_{14}=0$ but $c_{123}\ne 0$ for the first type and $c_{123}=0$ for the second type. For both types of black holes, in addition to the mass and charge of the black holes, we show that the presence of the æther field can also affect the size of the shadow. For the first type of black hole, it is shown that the shadow size increases with the parameter $c_{13}$, while for the second type of black hole, the shadow size still increases with $c_{13}$ but decreases with the parameter $c_{14}$. With these properties of the æther parameters, we also discuss the observational constraints on these parameters by using the data of the first black hole image by the Event Horizon Telescope. In addition, we also explore the effect of the æther field on the deflection angle of light and the time delay by using the Gauss-Bonnet theorem. It is shown that, for a specific combination $c_{123}=0$, the deflection angle/time delay is slightly affected by the æther parameter $c_{13}$ at the leading order.