On the existence of Killing vector fields

Abstract

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.

9 pages, no figure, to appear in Class. Quant. Grav

Cited by in corpus (14)

• On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• Stationary Black Holes as Holographs
• Symmetry inheritance of scalar fields
• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
• Symmetries of spacetime and their relation to initial value problems
• Stationary Black Holes as Holographs II
• Global and uniqueness properties of stationary and static spacetimes with outer trapped surfaces
• Conformal Killing Initial Data
• Neighbourhoods of Isolated Horizons and their stationarity
• A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory
• Space-time extensions II
• Closed conformal Killing-Yano initial data
• On Killing vectors in initial value problems for asymptotically flat space-times
• Killing and homothetic initial data for general hypersurfaces