Abstract. A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential L_ABCA' of an arbitrary symmetric spinor W_ABCD defined by W_ABCD = 2∇_(A^A'L_BCD)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 Ψ_ABCD 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 W_ABCD are identified: the first T_ABCD ( = T_(ABC)D) is given by L_ABCA' = ∇_A'^DT_ABCD, while the second H_ABA'B' ( = H_(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by L_ABCA' = ∇_(A^B'H_BC)A'B'. The superpotential T_ABCD is used to describe the gauge freedom in the Lanczos potential.

PACS numbers: 0420, 0240

Print publication: Issue 12 (21 June 2001)
Received 2 March 2001