Spacetimes Admitting Isolated Horizons

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  • 19 July 1999
Abstract
A general solution to the vacuum Einstein equations which admits the Ashtekar isolated horizon is characterized. It is a superposition -- in an exactly defined sense -- of the Schwarzschild metric with a certain free data 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, rotating in this case, horizon. More generally, a vacuum admitting any null, non expanding, shear free surface is characterized. The results are applied to show that, generically, the isolated horizon is not a Killing horizon and a spacetime is not spherically symmetric near the horizon even in the most symmetric non rotating case. The extension of the results to the non vacuum case, for instance the Maxwell-Einstein case, is easy modulo the lack of the existence and uniqueness statements.

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