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We obtain an exact Kerr-like black hole solution by solving the correspondinggravitational field equations in Einstein-bumblebee gravity model where Lorentzsymmetry is spontaneously broken once a vector field acquires a vacuumexpectation value. Results are presented for the purely radial Lorentz symmetrybreaking. In order to study the effects of this breaking, we consider the blackhole shadow and find that the radial of the unstable spherical orbit on theequatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$,and increases with $\ell<0$. These shifts are similar to those ofEinstein-aether black hole. The effect of the LV parameter on the black holeshadow is that it accelerates the appearance of shadow distortion, and could bedetected by the new generation of gravitational antennas.

Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking