Near-horizon local instability and quantum thermality

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