Physical Review · 1968 · 233 citations · 0 references
Natural SciencesPhysicsGravitationGravityRelativityEinstein Field EquationsGeneral RelativityGravitational FieldsMaxwell's EquationsNewtonian GravitationTwo-body ProblemEinstein Equations With Matter FieldsEinstein Field Equations In CosmologyGravitational Two-body ProblemMaxwell Equations In Covariant FormMaxwell's Equations In Covariant FormStationary Solutions
The field equations governing the gravitational field of a uniformly rotating axially symmetric source are reformulated in terms of a simple variational principle. The new formalism affords a concise unified derivation of the solutions discovered by Weyl and Papapetrou, and permits a simple derivation of the Kerr metric in terms of prolate spheroidal coordinates. More complex solutions are identified by applying perturbation theory.