  We revisit our previous proposed conjecture -- horizon creates a local
instability which acts as the source of quantum temperature of black hole. It
is found that a chargesless massless particle moving along the null trajectory
in Eddington-Finkelstein (EF) coordinates feels instability in the vicinity of
the horizon. Such instability is observer independent for this particle motion.
Moreover, an observer associated to EF coordinates finds the local Hamiltonian
as $xp$ where $p$ is the canonical momentum corresponding the coordinate $x$.
Finally, using this Hamiltonian we notice that at the quantum level this class
of observers feel the horizon as thermal object with temperature is given by
the Hawking expression. We provide this by using various techniques in quantum
mechanics and thereby bolstered our earlier claim -- the automatic local
instability can be a mechanism for emerging horizon as a thermal object. In
this process, the present analysis provides another set of coordinates (namely
EF frame), in addition to our earlier Painleve ones, in which the null
trajectory of the massless particle is governed by $xp$ type Hamiltonian in
near the horizon regime.
