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We investigate thermodynamic behaviors of the $D$-dimensional gravity coupledto a dynamical unit timelike vector, the aether, present two kinds of exactcharged solutions and study the linearized wave spectrum of this theory. Thereis an universal horizon behind the Killing horizon in these aether black holes.It is interesting that there exist $D$-dimensional Schwarzschild,Reissner-Nordstr\"{o}m and charged Schwarzschild black holes but now with anuniversal horizon inside. We find that in the uncharged case for both kinds, orcharged case but the charge $\bar Q\ll \bar r_0/2$ for the first kind, one canconstruct a Smarr formula and the (slightly modified) first law of black holemechanics at the universal horizons for the aether black holes. An entropy canbe associated with the universal horizon and a temperature can be definedthere. For the second kind aether black hole and for the first kind one in theextremal higher dimensions, the work term involving charge $V_{UH}\delta Q$disappeared. For aether wave, our results show that the spin-1 and spin-2 modesare the same as those in 4-dimensional spacetime, and only the spin-0 one isdifferent and dependant on the dimension number $n$.

Thermodynamical study on universal horizons in higher $D$-dimensional spacetime and aether waves