TL;DR
This paper establishes necessary and sufficient conditions for a 3-metric to originate from a static spacetime metric, under a genericity condition on the Ricci tensor.
Contribution
It provides a precise characterization of static 3-metrics in terms of Ricci tensor conditions, clarifying the geometric criteria for static spacetime realization.
Findings
Conditions are both necessary and sufficient for static metric realization
Requires a genericity condition on the Ricci tensor
Clarifies geometric criteria for static spacetimes
Abstract
Conditions are given which, subject to a genericity condition on the Ricci tensor, are both necessary and sufficient for a 3-metric to arise from a static spacetime metric.
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