On the proximity of black hole horizons: lessons from Vaidya

TL;DR

This paper introduces a geometric measure of the distance between apparent and event horizons in dynamical black hole spacetimes, demonstrating its physical relevance and behavior near equilibrium, with implications for black hole physics.

Contribution

It proposes a new, well-defined measure of horizon proximity in dynamical spacetimes and analyzes its properties in Vaidya spacetime.

Findings

The measure is well-defined and physically meaningful.

It behaves as expected in the near-equilibrium limit.

Implications for understanding black hole dynamics are discussed.

Abstract

In dynamical spacetimes, apparent and event horizons do not coincide. In this paper we propose a geometrical measure of the distance between those horizons and investigate it for the case of the Vaidya spacetime. We show that it is well-defined, physically meaningful, and has the expected behaviour in the near-equilibrium limit. We consider its implications for our understanding of black hole physics.