Cartan's equivalence method and null coframes in General Relativity

Details Cartan's equivalence method and null coframes in General Relativity Cartan's equivalence method and null coframes in General Relativity

2004-11-19

arxiv.org/abs/gr-qc/0411099v3

Class.Quant.Grav. 22 (2005) 1881-1901

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages. To be published in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/22/9/025

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) W\"unschmann Invariant. We show that the above mentioned construction naturally contains the Null Surface Formulation of General Relativity.

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