A pr 1 99 3 On completeness of orbits of Killing vector fields
نویسنده
چکیده
A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space–times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold.
منابع مشابه
v 1 1 4 O ct 2 00 3 ON THE THEORY OF KILLING ORBITS IN SPACE - TIME
This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instab...
متن کاملThe spinorial geometry of supersymmetric backgrounds
We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with s...
متن کاملOn Killing vector fields and Newman-Penrose constants
Asymptotically flat spacetimes with one Killing vector field are studied. The Killing equations are solved asymptotically using polyhomogeneous expansions (i.e. series in powers of 1/r and ln r), and solved order by order. The solution to the leading terms of these expansions yield the the asymptotic form of the Killing vector field. The possible classes of Killing fields are discussed by analy...
متن کاملROTATING DUST SOLUTIONS OF EINSTEIN’S EQUATIONS WITH 3-DIMENSIONAL SYMMETRY GROUPS PART 1: TWO KILLING FIELDS SPANNED ON u AND w
For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebański based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity...
متن کاملRotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups. I. Two Killing fields spanned on u and w
For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebański based on the Darboux theorem. In the resulting coordinates, the Killing vector fields ~if any exist! assume a special form. Each Killing vector field may be either spanned on the fields of velocity...
متن کامل