  In Einstein-aether theory, violating Lorentz invariance permits some
super-luminal communications, and the universal horizon can trap excitations
traveling at arbitrarily high velocities. To better understand the nature of
these universal horizons, we first modify the ray tracing method, and then use
it to study their surface gravity in charged Einstein-aether black hole
spacetime. Instead of the previous result in Ref. [Phys. Rev. D 89, 064061],
our results show that the surface gravity of the universal horizon is dependent
on the specific dispersion relation, $\kappa_{UH}=2(z-1)\kappa_{uh}/z$, where
$z$ denotes the power of the leading term in the superluminal dispersion
relation, characterizing different species of particles. And the associated
Hawking temperatures also are different with $z$. These findings, which
coincide with those in Ref. [Nucl. Phys. B 913, 694] derived by the tunneling
method, provide some full understanding of black hole thermodynamics in
Lorentz-violating theories.

General Relativity and Quantum Cosmology