Avenues for Analytic exploration in Axisymmetric Spacetimes. Foundations and the Triad Formalism

Understand

Axially symmetric spacetimes are the only models for isolated systems with continuous symmetries that also include dynamics.

• For such systems, we review the reduction of the vacuum Einstein field equations to their most concise form by dimensionally reducing to the three-dimensional space of orbits of the Killing vector, followed by a conformal rescaling.
• The resulting field equations can be written as a problem in three-dimensional gravity with a complex scalar field as source.
• This scalar field, the Ernst potential is constructed from the norm and twist of the spacelike Killing field.