Abstract
The classical Hamiltonian for a chargeless and massless particle in a very near-horizon region is shown to be of the form 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 “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.
- Received 15 November 2019
- Accepted 23 July 2020
DOI:https://doi.org/10.1103/PhysRevD.102.044006
© 2020 American Physical Society