TL;DR
This paper investigates vacuum Killing Initial Data on characteristic surfaces, proving a general theorem on the existence of Killing vectors in the domain of dependence and analyzing special cases like bifurcate horizons.
Contribution
It introduces a general theorem for the existence of Killing vectors from initial data on characteristic surfaces, expanding understanding of spacetime symmetries.
Findings
Proved a general theorem on Killing vector existence.
Analyzed special cases including bifurcate horizons.
Enhanced understanding of vacuum spacetime symmetries.
Abstract
We analyze vacuum Killing Initial Data on characteristic Cauchy surfaces. A general theorem on existence of Killing vectors in the domain of dependence is proved, and some special cases are analyzed in detail, including the case of bifurcate Killing horizons.
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