Near horizon local instability and quantum thermality

TL;DR

This paper demonstrates that near the black hole horizon, a massless particle experiences an observer-independent local instability, which leads to a thermal spectrum consistent with Hawking temperature, supporting the idea that horizon instability underpins black hole thermality.

Contribution

It introduces a new coordinate framework (Eddington-Finkelstein) showing the horizon's local instability causes thermal behavior, extending previous Painleve coordinate analysis.

Findings

Null particles near the horizon exhibit observer-independent instability.

The local Hamiltonian near the horizon takes an $xp$ form.

Quantum analysis reveals the horizon appears thermal with Hawking temperature.

Abstract

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.