Investigating rotating black holes in bumblebee gravity: insights from EHT observations

The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87* and these results are consistent with the shadow of a Kerr black hole as predicted by general relativity. However, Kerr-like rotating black holes in modified gravity theories can not ruled out, as they provide a crucial testing ground for these theories through EHT observations. It motivates us to investigate the bumblebee theory, a vector-tensor extension of the Einstein-Maxwell theory that permits spontaneous symmetry breaking, resulting in the field acquiring a vacuum expectation value and introducing Lorentz violation. We present rotating black holes within this bumblebee gravity model, which includes an additional parameter ℓ alongside the mass M and spin parameter a — namely RBHBG. Unlike the Kerr black hole, an extremal RBHBG, for ℓ < 0, refers to a black hole with angular momentum a > M. We derive an analytical formula necessary for the shadow of our rotating black holes, then visualize them with varying parameters a and ℓ, and also estimate the black hole parameters using shadow observables viz. shadow radius Rs, distortion δs, shadow area A and oblateness D using two well-known techniques. We find that ℓ incrementally increases the shadow size and causes more significant deformation while decreasing the event horizon area. Remarkably, an increase in ℓ enlarges the shadow radius irrespective of spin or inclination angle θ0.