The recently obtained hairy Kerr black holes, due to additional sources or surrounding fluid, like dark matter, with conserved energy-momentum tensor, have a deviation α and primary hair l0, apart from rotation parameter a and mass M. In the wake of the Event Horizon Telescope (EHT) observations of the supermassive black hole M87*, a recent surge in interest in black hole shadows suggests comparing the black holes in general relativity and modified theories of gravity to assess these models’ differences. Motivated by this, we take on an extensive study of the rotating hairy Kerr black holes, which encompasses, in particular cases, the Kerr black hole (α = 0). We investigate ergosphere and shadows of the black holes to infer that their size and shape are affected due to the l0 and are found to harbour a richer chaotic structure. In particular, the hairy Kerr black holes possess smaller size but more distorted shadows when compared with Kerr black holes. We also estimate the parameters l0 and a associated with hairy Kerr black holes using the shadow observables. The inferred circularity deviation ΔC ≤ 0.1 for the M87* black hole is satisfied, whereas shadow angular diameter θd = 42 ± 3μas, within 1σ region, for a given choice of α, places bounds on the parameters a and l0. Interestingly, the shadow axial ratio obeying 1 < Dx ≲ 4/3 is in agreement with the EHT results and thus eventuates in the hairy Kerr black holes being suitable candidates for astrophysical black holes.

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 recently unveiled the first image of the supermassive black hole M87*, which exhibited a ring of angular diameter θ d = 42 ± 3 μas, a circularity deviation of ΔC ≤ 0.1, and also inferred a black hole mass of M = (6.5 ± 0.7) × 109 M ⊙. This provides a new window onto tests of theories of gravity in the strong-field regime, including probes of violations of the no-hair theorem. It is widely believed that the Kerr metric describes astrophysical black holes, as encapsulated in the critical but untested no-hair theorem. Modeling Horndeski gravity black holes—with an additional hair parameter h besides the mass M and spin a of the Kerr black hole—as the supermassive black hole M87*, we observe that to be a viable astrophysical black hole candidate, the EHT result constrains the (a, h) parameter space. However, a systematic bias analysis indicates that rotating Horndeski black hole shadows may or may not capture Kerr black hole shadows, depending on the parameter values; the latter is the case over a substantial part of the constrained parameter space, allowing Horndeski gravity and general relativity to be distinguishable in the said space, and opening up the possibility of potential modifications to the Kerr metric.

The Event Horizon Telescope (EHT) collaboration’s image of the compact object at the Galactic center is the first direct evidence of the supermassive black hole (BH) Sgr A*. The shadow of Sgr A* has an angular diameter d sh = 48.7 ± 7 μas with fractional deviation from the Schwarzschild BH shadow diameter δ = − 0.08 − 0.09 + 0.09 , − 0.04 − 0.10 + 0.09 (for the VLTI and Keck mass-to-distance ratios). Sgr A*'s shadow size is within 10% of Kerr predictions, equipping us with yet another tool to analyze gravity in the strong-field regime, including testing loop quantum gravity (LQG). We use Sgr A*'s shadow to constrain the metrics of two well-motivated LQG-inspired rotating BH (LIRBH) models characterized by an additional deviation parameter L q , which recover the Kerr spacetime in the absence of quantum effects (L q → 0). When increasing the quantum effects through L q , the shadow size increases monotonically, while the shape gets more distorted, allowing us to constrain the fundamental parameter L q . We use the astrophysical observables shadow area A and oblateness D to estimate the BH parameters. It may be useful in extracting additional information about LIRBHs. While the EHT observational results completely rule out the wormhole region in LIRBH-2, a substantial parameter region of the generic BHs in both models agrees with the EHT results. We find that the upper bounds on L q obtained from the shadow of Sgr A*—L q ≲ 0.0423 and L q ≲ 0.0821 for the two LIRBHs, respectively—are more stringent than those obtained from the EHT image of M87*.

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable.