Isolated Horizon, Killing Horizon and Event Horizon

TL;DR

This paper explores the relationships between isolated, Killing, and event horizons in space-times, establishing conditions under which isolated horizons are Killing horizons and analyzing their possible configurations.

Contribution

It provides new criteria for when an isolated horizon is also a Killing horizon and examines the relative positioning of horizons in space-times with multiple horizon types.

Findings

Isolated horizon is a Killing horizon if it admits a stationary neighborhood.

A Killing horizon is always an isolated horizon.

All relative positions of isolated and event horizons are possible under certain conditions.

Abstract

We consider space-times which in addition to admitting an isolated horizon also admit Killing horizons with or without an event horizon. We show that an isolated horizon is a Killing horizon provided either (1) it admits a stationary neighbourhood or (2) it admits a neighbourhood with two independent, commuting Killing vectors. A Killing horizon is always an isolated horizon. For the case when an event horizon is definable, all conceivable relative locations of isolated horizon and event horizons are possible. Corresponding conditions are given.