Fredrik Andersson and S Brian Edgar 2001 Class. Quantum Grav. 18 2297 doi:10.1088/0264-9381/18/12/304
Fredrik Andersson and S Brian Edgar
Show affiliationsA new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2∇(AA'LBCD)A'; this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ΨABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD ( = T(ABC)D) is given by LABCA' = ∇A'DTABCD, while the second HABA'B' ( = H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ∇(AB'HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.
04.20.Gz Spacetime topology, causal structure, spinor structure
04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
Issue 12 (21 June 2001)
Received 2 March 2001
Fredrik Andersson and S Brian Edgar 2001 Class. Quantum Grav. 18 2297
I Shlimak et al 2001 J. Phys.: Condens. Matter 13 6059
James Feigenbaum 2003 Rep. Prog. Phys. 66 1611
X M Tong and S I Chu 1999 J. Phys. B: At. Mol. Opt. Phys. 32 5593
R M Wentzcovitch and M L Cohen 1986 J. Phys. C: Solid State Phys. 19 6791
I Jensen and A J Guttmann 1996 J. Phys. A: Math. Gen. 29 3817
Iwan Jensen and Anthony J Guttmann 1999 J. Phys. A: Math. Gen. 32 4867
Stephen C Anco 2003 J. Phys. A: Math. Gen. 36 8623
R Gaudoin et al 2002 J. Phys.: Condens. Matter 14 8787
M. J. Pivovaroff et al. 2001 ApJ 554 161