Emanuel Gallo et al 2004 Class. Quantum Grav. 21 4063 doi:10.1088/0264-9381/21/17/004
Emanuel Gallo1, Carlos Kozameh1, Ezra T Newman2 and Kiplin Perkins2
Show affiliationsWe explore the different geometric structures that can be constructed from the class of pairs of second-order PDEs that satisfy the condition of a vanishing generalized Wünschmann invariant. This condition arises naturally from the requirement of a vanishing torsion tensor. In particular, we find that from this class of PDEs we can obtain all four-dimensional conformal Lorentzian metrics as well as all Cartan normal conformal O(4, 2) connections. To conclude, we briefly discuss how the conformal Einstein equations can be imposed by further restricting our class of PDEs to those satisfying additional differential conditions.
02.30.Jr Partial differential equations
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 17 (7 September 2004)
Received 1 April 2004
Published 10 August 2004
Emanuel Gallo et al 2004 Class. Quantum Grav. 21 4063
A Feinstein et al 2000 Class. Quantum Grav. 17 3599
Takeshi Odagiri et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 225101
N Abd el All et al 2009 J. Phys.: Conf. Ser. 190 012066
Olivier Bernus et al 2002 Phys. Med. Biol. 47 1947
D Hartley et al 1991 J. Phys. A: Math. Gen. 24 5253
M. Dickinson et al 2004 ApJ 600 L99
Hui-Wen Cheng and Yiming Li 2009 Semicond. Sci. Technol. 24 115021
2002 J. Phys.: Condens. Matter 14
W Taweepreda et al 2009 J. Phys.: Conf. Ser. 190 012150