Higher dimensional conformal metrics from PDEs and Null Surface Formulation of GR

Details Higher dimensional conformal metrics from PDEs and Null Surface Formulation of GR Higher dimensional conformal metrics from PDEs and Null Surface Formulation of GR

2011-11-14

arxiv.org/abs/1111.3232v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages. arXiv admin note: substantial text overlap with arXiv:gr-qc/0502102

Scientific paper

We analyze the relationship between $n$-dimensional conformal metrics and a certain class of partial differential equations (PDEs) that are in duality with the eikonal equation. In particular, we extend the Null Surface Formulation of General Relativity to higher dimensions and give explicit expressions for the components of the metric and the generalized W\"{u}nschmann-like metricity conditions. In general, this extension gives indefinite metrics and it is not so simple to write explicit conditions in order to assure the metrics be Lorentzian one. We also compute the equation that the conformal factor must satisfy in order the metric be a solution of the Einstein equations.

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