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In mimetic gravity, we derive $D$-dimension charged black hole solutionshaving flat or cylindrical horizons with zero curvature boundary. Theasymptotic behaviours of these black holes behave as (A)dS. We study bothlinear and nonlinear forms of the Maxwell field equations in two separatecontexts. For the nonlinear case, we derive a new solution having a metric withmonopole, dipole and quadrupole terms. The most interesting feature of thisblack hole is that its dipole and quadruple terms are related by a constant.However, the solution reduces to the linear case of the Maxwell field equationswhen this constant acquires a null value. Also, we apply a coordinatetransformation and derive rotating black hole solutions (for both linear andnonlinear cases). We show that the nonlinear black hole has stronger curvaturesingularities than the corresponding known black hole solutions in generalrelativity. We show that the obtained solutions could have at most twohorizons. We determine the critical mass of the degenerate horizon at which thetwo horizons coincide. We study the thermodynamical stability of the solutions.We note that the nonlinear electrodynamics contributes to process asecond-order phase transition whereas the heat capacity has an infinitediscontinuity.

Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity