General higher-order rogue waves in the space-shifted $\mathcal{PT}$-symmetric nonlocal nonlinear SchrÖdinger equation

General higher-order rogue wave solutions to the space-shifted$\mathcal{PT}$-symmetric nonlocal nonlinear Schrödinger equation are constructed by employing the Kadomtsev-Petviashvili hierarchy reduction method.The analytical expressions for rogue wave solutions of any$N$th-order are given through Schur polynomials.We first analyze the dynamics of the first-order rogue waves,and find that the maximum amplitude of the rogue waves can reach any height larger than three times of the constant background amplitude.The effects of the space-shifted factor$x_0$of the$\mathcal{PT}$-symmetric nonlocal nonlinear Schrödinger equation in the first-order rogue wave solutions are studied,which only changes the center positions of the rogue waves.The dynamical behaviours and patterns of the second-order rogue waves are also analytically investigated.Then the relationships between$N$th-order rogue wave patterns and the parameters in the analytical expressions of the rogue wave solutions are given,and the several different patterns of the higher-order rogue waves are further shown.