Cartan's equivalence method and null coframes in general relativity

EMANUEL GALLO, MIRTA IRIONDO, CARLOS KOZAMEH

CLASSICAL AND QUANTUM GRAVITY

Institute of Physics Publishing

Lugar: Bristol; Año: 2005 vol. 22 p. 1881 - 1901

0264-9381

Using Cartan´s equivalence method for point transformations we obtain from first principles the conformal geometry associated with third order ODEs and a special class of PDEs in two dimensions. We explicitly construct the null tetrads of a family of Lorentzian metrics, the conformal group in three and four dimensions and the so called normal metric connection. A special feature of this connection is that the non vanishing components of its torsion depend on one relative invariant, the (generalized) Wünschmann Invariant. We show that the abovementioned construction naturally contains the Null Surface Formulation of General Relativity.