Uniqueness of static black-holes without analyticity

TL;DR

This paper proves that the analyticity assumption is unnecessary for the uniqueness of static black holes and demonstrates that certain prehorizons cannot exist in well-behaved domains.

Contribution

It removes the analyticity requirement from static black hole uniqueness proofs and rules out specific prehorizon structures in well-behaved domains.

Findings

Analyticity is not needed for static black hole uniqueness.

Prehorizons covering closed sets cannot occur in well-behaved domains.

The results extend the understanding of black hole uniqueness without strong regularity assumptions.

Abstract

We show that the hypothesis of analyticity in the uniqueness theory of vacuum, or electrovacuum, static black holes is not needed. More generally, we show that prehorizons covering a closed set cannot occur in well-behaved domains of outer communications.