The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

TL;DR

This paper proves that the only static, vacuum, asymptotically flat black hole solutions with regular horizons are the Schwarzschild solutions, completing their classification in this setting.

Contribution

It establishes the non-existence of degenerate horizon components in static vacuum black holes, confirming Schwarzschild solutions as the unique exteriors.

Findings

Schwarzschild black holes are the only static, vacuum, asymptotically flat solutions with regular horizons.

Degenerate horizon components do not exist in such solutions.

The classification of static vacuum black holes is complete under the given conditions.

Abstract

We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole space-times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space-times, showing that the domains of outer communication of the Schwarzschild black holes exhaust the space of appropriately regular black hole exteriors.