Discussion on Event Horizon and Quantum Ergosphere of Evaporating Black Holes in a Tunnelling Framework

TL;DR

This paper analyzes the relationship between event horizons, apparent horizons, and Hawking radiation in evaporating black holes using a tunnelling framework, revealing that the quantum ergosphere aligns with the tunnelling barrier and radiation originates from the apparent horizon.

Contribution

It demonstrates that the event and apparent horizons correspond to tunnelling barrier turning points, providing new insights into black hole radiation mechanisms within a tunnelling framework.

Findings

Event horizon and apparent horizon correspond to tunnelling barrier turning points.

Quantum ergosphere coincides with the tunnelling barrier.

Hawking radiation originates from the apparent horizon.

Abstract

In this paper, with the Parikh-Wilczek tunnelling framework the positions of the event horizon of the Vaidya black hole and the Vaidya-Bonner black hole are calculated respectively. We find that the event horizon and the apparent horizon of these two black holes correspond respectively to the two turning points of the Hawking radiation tunnelling barrier. That is, the quantum ergosphere coincides with the tunnelling barrier. Our calculation also implies that the Hawking radiation comes from the apparent horizon.