English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The celebrated uniqueness's theorem of the Schwarzschild solution by Israel,Robinson et al, and Bunting/Masood-ul-Alam, asserts that the onlyasymptotically flat static solution of the vacuum Einstein equations withcompact but non-necessarily connected horizon is Schwarzschild. Between thisarticle and its sequel we extend this result by proving a classificationtheorem for all (metrically complete) solutions of the static vacuum Einsteinequations with compact but non-necessarily connected horizon without making anyfurther assumption on the topology or the asymptotic. It is shown that any suchsolution is either: (i) a Boost, (ii) a Schwarzschild black hole, or (iii) isof Myers/Korotkin-Nicolai type, that is, it has the same topology and Kasnerasymptotic as the Myers/Korotkin-Nicolai black holes. In a broad sense, thetheorem classifies all the static vacuum black holes in 3+1-dimensions. In thisPart I we use introduce techniques in conformal geometry and comparisongeometry \'a la Bakry-\'Emery to prove that vacuum static black holes have onlyone end, and, furthermore, that the lapse is bounded away from zero atinfinity. The techniques have interest in themselves and could be applied inother contexts as well, for instance to study higher-dimensional static blackholes.

A classification theorem for static vacuum black holes. Part I: the study of the lapse