4D Conformal metrics, the eikonal equation and fourth-order ODEs

Details 4D Conformal metrics, the eikonal equation and fourth-order ODEs 4D Conformal metrics, the eikonal equation and fourth-order ODEs

Dec 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cqgra..22.5073m&link_type=abstract

Classical and Quantum Gravity, Volume 22, Issue 23, pp. 5073-5088 (2005).

Physics

Scientific paper

In this work we show that on the space of solutions of a certain class of fourth-order ODEs, u'''' = Λ(s, u, u', u'', u'''), a four-dimensional conformal metric, gab, can be constructed such that the four-dimensional eikonal equation, gabu,au,b = 0, holds. Furthermore, we remark that this structure is invariant under contact transformations. Our general results are applied to the Minkowski spacetime.

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