Killing Initial Data
arXiv:gr-qc/9604040 · doi:10.1088/0264-9381/14/1A/007
Abstract
We study space-time Killing vectors in terms of their "lapse and shift" relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse-shift pairs, which we call Killing initial data (KID'S), to form a Lie algebra under the bracket operation induced by the Lie commutator of vector fields on space-time. This result is applied to obtain a theorem on the periodicity of orbits for a class of Killing vector fields in asymptotically flat space-times.
17 pages
References in corpus (2)
Cited by in corpus (51)
- Existence of non-trivial, vacuum, asymptotically simple space-times
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Construction of N-body initial data sets in general relativity
- Geometric inequalities for axially symmetric black holes
- Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
- Symmetry-seeking spacetime coordinates
- On the construction of a geometric invariant measuring the deviation from Kerr data
- Killing vectors in asymptotically flat space--times: II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
- Initial data sets for the Schwarzschild spacetime
- Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
- Positive mass theorems for asymptotically AdS spacetimes with arbitrary cosmological constant
- Manifold structures for sets of solutions of the general relativistic constraint equations
- On marginally outer trapped surfaces in stationary and static spacetimes
- Killing spinor initial data sets
- Kerr Initial data
- Numerical Relativity in 3+1 Dimensions
- Hypersurface data: General properties and Birkhoff theorem in spherical symmetry
- CMC-Slicings of Kottler-Schwarzschild-de Sitter Cosmologies
- Static potentials on asymptotically flat manifolds
- Gluing construction of initial data with Kerr-de Sitter ends
- A local non-negative initial data scalar characterisation of the Kerr solution
- KIDs like cones
- Vacuum type D initial data
- Unique continuation and extensions of Killing vectors at boundaries for stationary vacuum space-times
- Non-stationary Energy in General Relativity
- Symmetry and instability of marginally outer trapped surfaces
- Conformal Killing Initial Data
- Symmetries of the asymptotically de Sitter spacetimes
- Lorentz Invariance in Shape Dynamics
- Existence of gradient CKV and gradient conformally stationary LRS spacetimes
- A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors
- KIDs prefer special cones
- Dain's invariant on non-time symmetric initial data sets
- Covariant classification of conformal Killing vectors of locally conformally flat -manifolds with an application to Kerr-de Sitter
- Killing boundary data for anti-de Sitter-like spacetimes
- Dain's invariant for black hole initial data
- Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector
- Small deformations of extreme five dimensional Myers-Perry black hole initial data
- Non-stationary Energy of Perfect Fluid Sources in General Relativity
- A note on mass-minimising extensions
- Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. II. KIDs for the Kerr-(A)(de Sitter) family
- A geometric invariant characterising initial data for the Kerr-Newman spacetime
- Uniqueness theorems for static spacetimes containing marginally outer trapped surfaces
- Closed conformal Killing-Yano initial data
- Constraints and Time Evolution in Generic (Riemann) Gravity
- Killing Initial Data on Totally Umbilical & Compact Hypersurfaces
- Killing and homothetic initial data for general hypersurfaces
- The problem of characterising stationary data for the vacuum Einstein equations
- Twistor initial data characterisation of pp-waves
- -wave initial data
- On a lower-dimensional Killing vector origin of irreducible Killing tensors