  In this paper, we study the existence of universal horizons in a given static
spacetime, and find that the test khronon field can be solved explicitly when
its velocity becomes infinitely large, at which point the universal horizon
coincides with the sound horizon of the khronon. Choosing the timelike
coordinate aligned with the khronon, the static metric takes a simple form,
from which it can be seen clearly that the metric is free of singularity at the
Killing horizon, but becomes singular at the universal horizon. Applying such
developed formulas to three well-known black hole solutions, the Schwarzschild,
Schwarzschild anti-de Sitter, and Reissner-Nordstr\"om, we find that in all
these solutions universal horizons exist and are always inside the Killing
horizons. In particular, in the Eddington-Finkelstein and Painleve-Gullstrand
coordinates, in which the metrics are not singular when crossing both of the
Killing and universal horizons, the peeling-off behavior of the khronon is
found only at the universal horizons, whereby we show that the values of
surface gravity of the universal horizons calculated from the peeling-off
behavior of the khronon match with those obtained from the covariant definition
given recently by Cropp, Liberati, Mohd and Visser.
