Horizon induces instability locally and creates quantum thermality

TL;DR

This paper demonstrates that near a black hole horizon, the classical particle Hamiltonian resembles xp, leading to local instability and quantum thermality, with the temperature matching Hawking's prediction, suggesting instability causes horizon temperature.

Contribution

It reveals that horizon-induced instability at the classical level results in quantum thermality, providing a new physical mechanism for horizon temperature.

Findings

Hamiltonian near horizon is of the form xp for radial motion

Local instability arises due to horizon effects

Quantum analysis yields Hawking temperature

Abstract

The classical Hamiltonian for a chargeless and massless particle in a very near horizon region is shown to be of the form $H\sim xp$ as long as radial motion is concerned. This is demonstrated explicitly for static spherically symmetric black hole and also found to be applicable for specific choice of radial trajectories in the Kerr case. Such feature of horizon leads to unavoidable "{\it local instability}" in the particle's radial motion as long as near horizon regime is concerned. We show that at the quantum level this provides thermality in the system. The temperature is found to be given by the Hawking expression. Finally, we conjecture that the automatic instability created by the horizon is responsible for its own temperature and consequently can be a possible physical mechanism for horizon temperature.