Killing vector analysis in GHP formalism of conformally flat pure radiation metrics with negative cosmological constant

Abstract

In a paper by Edgar and Ludwig it was shown how the symmetry analysis of a spacetime may be considerably simpli ed when using intrinsic GHP tetrads. A generalised Lie derivative operator, that reduces to the usual Lie derivative when acting on zero-weighted quantities, was introduced. The Killing equations are then obtained by acting with the commutators of this derivative and the GHP operators on zero-weighted scalars (the intrinsic coordinates). In this work we extend the method to a class of spacetimes with null rotation isotropy, where an intrinsic GHP tetrad cannot be completly found. The Killing vectors of the conformally at pure radiation metrics with negative cosmological constant arethen determined and the result is compared with other methods.