Symmetries of spacetime and their relation to initial value problems

Abstract

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential equations can be deduced from the matter field equations. Second, gravity is supposed to be coupled to the matter fields by requiring that the Ricci tensor is a smooth function of the basic matter field variables and the metric. It is shown then that the ``time'' evolution of these type of gravity-matter systems preserves the symmetries of initial data specifications.

12 pages, to appear in Class. Quant. Grav

References in corpus (4)

• On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• On the existence of Killing vector fields
• On Killing vectors in initial value problems for asymptotically flat space-times

Cited by in corpus (10)

• Stationary Black Holes as Holographs
• Symmetry inheritance of scalar fields
• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
• 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