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In this paper, a Bondi-Hoyle accretion onto the rotating black hole inEinstein-Gauss Bonnet gravity is studied. By injecting the gas from theupstream region of the computational domain, we have found the occurrence ofthe stable shock cones in the downstream region. The dynamical structures andoscillation properties of these shock cones strongly depend on the black holespin parameter $a$ and Gauss-Bonnet coupling constant alpha. It is found thatthe various values of alpha can lead the different amounts of matter to pile upclose to the black hole horizon, higher alpha causes bigger oscillationamplitude in the mass accretion rate, and the required time to reach thesteady-state is getting smaller with the increase in alpha. Moreover,increasing alpha in the negative direction causes a decrease in the shockopening angle and this angle slightly increases with the increasing $\alpha$ inthe positive direction. We found that the negative values of Gauss-Bonnetcoupling constant are more favored to have interesting physical outcomes suchas accretion rate and oscillation. In addition, the higher the black holerotation parameter (a) emerges the higher the accretion rate. It is alsoconfirmed that, for alpha \rightarrow 0, the black hole solution in EGB gravityconverges to Kerr in general relativity. Furthermore, Gauss-Bonnet couplingconstant could be used to constrain the size of the observed shadow of M87*radius for various values of the black hole rotation parameter.

Dynamical Evolution of the Shock Cone around $4D$ Einstein-Gauss Bonnet Rotating Black Hole