A note on static metrics: the degenerate case
Joan Josep Ferrando, Juan Antonio S\'aez
TL;DR
This paper characterizes the conditions under which a 3-metric can serve as the spatial metric of a static vacuum solution, extending previous work to include degenerate cases.
Contribution
It provides necessary and sufficient conditions for degenerate 3-metrics to be the adapted spatial metrics of static vacuum solutions, completing the understanding for all cases.
Findings
Derived conditions for degenerate 3-metrics
Extended previous regular case results to degenerate cases
Clarified the geometric structure of static vacuum solutions
Abstract
We give the necessary and sufficient conditions for a 3-metric to be the adapted spatial metric of a static vacuum solution. This work accomplishes for the degenerate cases the already known study for the regular ones (Bartnik and Tod 2006 {\it Class. Quantum Grav.} {\bf 23} 569-571).
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