Space-Times Admitting Isolated Horizons

TL;DR

This paper characterizes vacuum solutions to Einstein's equations with isolated horizons, demonstrating a superposition approach that confirms Ashtekar's conjecture and extends to Kerr and other null surface spacetimes.

Contribution

It introduces a superposition method for vacuum solutions with isolated horizons, confirming conjectures and extending to Kerr and null surface cases.

Findings

Superposition of Schwarzschild with free data describes isolated horizons.

Kerr metric admits a class of solutions with isolated horizons.

Non-rotating isolated horizons generally lack Killing vectors and spherical symmetry.

Abstract

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar's conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non expanding, shear free surface is characterized. The results are applied to show that, generically, the non-rotating isolated horizon does not admit a Killing vector field and a spacetime is not spherically symmetric near a symmetric horizon.