Charged Einstein-\ae ther black holes in $n$-dimensional spacetime

In this work, we investigate the $n$-dimensional charged static black hole solutions in the Einstein-\ae ther theory. By taking the metric parameter $k$ to be $1,0$, and $-1$, we obtain the spherical, planar, and hyperbolic spacetimes respectively. Three choices of the cosmological constant, $\Lambda>0$, $\Lambda=0$ and $\Lambda<0$, are investigated, which correspond to asymptotically de Sitter, flat and anti-de Sitter spacetimes. The obtained results show the existence of the universal horizon in higher dimensional cases which may trap any particle with arbitrarily large velocity. We analyze the horizon and the surface gravity of 4- and 5-dimensional black holes, and the relations between the above quantities and the electrical charge. It is shown that when the aether coefficient $c_{13}$ or the charge $Q$ increases, the outer Killing horizon shrinks and approaches the universal horizon. Furthermore, the surface gravity decreases and approaches zero in the limit $c_{13}\rightarrow\infty$ or $Q\rightarrow Q_e$, where $Q_e$ is the extreme charge. The main features of the horizon and surface gravity are found to be similar to those in $n=3$ case, but subtle differences are also observed.