Flat deformation of a spacetime admitting two Killing fields

Abstract

It is shown that given an analytic Lorentzian metric on a 4-manifold, $g$, which admits two Killing vector fields, then it exists a local deformation law $\eta =ag+bH$, where $H$ is a 2-dimensional projector, such that $\eta$ is flat and admits the same Killing vectors. We also characterize the particular case when the projector $H$ coincides with the quotient metric. We apply some of our results to general stationary axisymmetric spacetimes

References in corpus (4)

• On the classification of type D spacetimes
• Bi-conformal vector fields and their applications
• Flat deformation theorem and symmetries in spacetime
• On the degrees of freedom of a semi-Riemannian metric

Cited by in corpus (1)

• Deformations of three-dimensional metrics