  We consider universal properties that arise from a local geometric structure
of a Killing horizon. We first introduce a non-perturbative definition of such
a local geometric structure, which we call an asymptotic Killing horizon. It is
shown that infinitely many asymptotic Killing horizons reside on a common null
hypersurface, once there exists one asymptotic Killing horizon. The
acceleration of the orbits of the vector that generates an asymptotic Killing
horizon is then considered. We show that there exists the $\textit{diff}(S^1)$
or $\textit{diff}(R^1)$ sub-algebra on an asymptotic Killing horizon
universally, which is picked out naturally based on the behavior of the
acceleration. We also argue that the discrepancy between string theory and the
Euclidean approach in the entropy of an extreme black hole may be resolved, if
the microscopic states responsible for black hole thermodynamics are connected
with asymptotic Killing horizons.
