The shadows of accelerating Kerr-Newman black hole and constraints from M87*

In this paper, we study the influence of the parameters for the accelerating Kerr-Newman black hole on the shadows and the constraints, extensively. We find that the rotating parameter a, the charge parameter e, and the inclination angle θ0 affect the shadow qualitatively similar to that of Kerr-Newman black holes. The result shows that the size of the shadow will scale down with the accelerating factor A. Besides, the factor A also can affect the best viewing angles, which make the observations maximum deviate from θ0=π2, and the degree of the deviations are less than 1%. Then, we assume the M87* as an accelerating Kerr-Newman black hole with the mass M=6.5×109M⊙ and the distance r0=16.8Mpc. Combining the EHT observations, we find that neither the observations, circularity deviation ΔC or axial ratio Dx can distinguish the accelerating black hole or not. However, the characteristic areal-radius of the shadow curve Ra can give corresponding constraints on the parameters of the accelerating Kerr-Newman black hole. The result shows that the bigger accelerating factor A is, the stronger constraints on the rotating parameter a and charged parameter e. The maximum range of the accelerating factor is Ar0≤0.558 for a accelerating Schwarzschild case with (a/M=e/M=0), and for an extremely slow accelerating case (Ar0≤0.01), the ranges of rotating parameter a and charged parameter e are a/M∈(0,1) and e/M∈(0,0.9).