G S Hall 2003 Class. Quantum Grav. 20 4067 doi:10.1088/0264-9381/20/18/313
G S Hall
Show affiliationsThis paper gives a theoretical discussion of the orbits and isotropies which arise in a spacetime 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 spacetime in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of 'stable' orbits and the possible misbehaviour of the 'unstable' ones is pointed out and, in particular, the fact that independent Killing vector fields in spacetime may not induce independent Killing vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 18 (21 September 2003)
Received 4 June 2003
Published 29 August 2003
G S Hall 2003 Class. Quantum Grav. 20 4067
Jens Bolte and Jonathan Harrison 2003 J. Phys. A: Math. Gen. 36 2747
Raffaele Rani et al 2003 Class. Quantum Grav. 20 1929
E. L. Wright et al. 2009 ApJS 180 283
E Minguzzi 2003 Class. Quantum Grav. 20 2443
Markus J Buehler et al 2004 Modelling Simul. Mater. Sci. Eng. 12 S391
J. Dunkley et al. 2009 ApJS 180 306
B. Gold et al. 2009 ApJS 180 265
Brian G Spratt 2002 J. Radiol. Prot. 22 125
Alfonso García-Parrado and José M M Senovilla 2003 Class. Quantum Grav. 20 L139