Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*

ABSTRACT 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.

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