The new potential for the Weyl tensor in N dimensions: gauge and wave equation

¹ Matematiska Institutionen, Linköpings Universitet, 581 83, Linköping, Sweden
² Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain

Abstract

Although the Lanczos potential (a (2,1) form, L_ab^c) for the Weyl tensor does not exist in dimensions greater than four, a new potential (a (2,3) form, P_ab^cde, which coincides with the double dual of L_ab^c in four dimensions) has recently been shown to exist in all dimensions n ≥ 4. In this talk we investigate the question of gauge and discuss the structure of the new potential's wave equation which is obtained from the Bianchi identities; identifying the gauge supplies us with a new direct proof of the existence of P_ab^cde via the Cauchy-Kowaleski theorem, as well as the foundation for more general investigations of the first order symmetric hyperbolic structure.