On the local extension of Killing vector-fields in Ricci flat manifolds

TL;DR

This paper investigates the conditions under which Killing vector-fields can be extended locally in smooth Ricci flat manifolds, highlighting implications for black hole rigidity in general relativity.

Contribution

It provides new insights into the extension problem of Killing vector-fields in Ricci flat manifolds, with relevance to black hole rigidity.

Findings

Extension criteria for Killing vector-fields established

Implications for black hole rigidity discussed

Revisits classical extension problems in differential geometry

Abstract

We revisit the problem of extension of Killing vector-fields in smooth Ricci flat manifolds, and its relevance to the black hole rigidity problem.