Is instability near a black hole key for "thermalization'' of its horizon?

TL;DR

This paper proposes a theoretical model where the inherent instability of the near-horizon Hamiltonian leads to the thermalization of the black hole horizon, providing a potential explanation for horizon thermalization.

Contribution

It introduces a model linking horizon instability with thermalization, using a $xp$ type Hamiltonian to explain observer-dependent thermal effects.

Findings

Near-horizon Hamiltonian is unstable and induces thermalization.

Thermalization is demonstrated in both Schrödinger and Heisenberg pictures.

Instability near the horizon may explain black hole thermalization.

Abstract

We put forward an attempt towards building a possible theoretical model to understand the observer dependent thermalization of black hole horizon. The near horizon Hamiltonian for a massless, chargeless particle is $xp$ type. This is unstable in nature and so the horizon can induce instability in a system. The particle in turn finds the horizon thermal when it interacts with it. We explicitly show this in the Schrodinger as well as in Heisenberg pictures by taking into account the time evolution of the system under this Hamiltonian. Hence we postulate that existing instability near the horizon can be one of the potential candidates for explaining the black hole thermalization.