On the Near-Horizon Geometry of an Evaporating Black Hole

TL;DR

This paper investigates the near-horizon geometry of evaporating black holes using semi-classical Einstein equations, emphasizing the role of vacuum energy-momentum and Hawking radiation in a dynamic, spherically symmetric setting.

Contribution

It provides a detailed analysis of the time-dependent near-horizon geometry considering vacuum back-reaction, advancing understanding of black hole evaporation.

Findings

Vacuum energy-momentum significantly influences the near-horizon structure.

Hawking radiation's back-reaction alters the apparent horizon dynamics.

The study offers a semi-classical geometric description of evaporating black holes.

Abstract

The near-horizon geometry of evaporation black holes is determined according to the semi-classical Einstein equation. We consider spherically symmetric configurations in which the collapsing star has already collapsed below the Schwarzschild radius. The back-reaction of the vacuum energy-momentum, including Hawking radiation, is taken into account. The vacuum energy-momentum plays a crucial role in a small neighborhood of the apparent horizon, as it appears at the leading order in the semi-classical Einstein equation. Our study is focused on the time-dependent geometry in this region.