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Covariant double-null dynamics: $(2+2)$-splitting of the Einstein equations

P. R. Brady·S. Droz·W. Israel·S. M. Morsink
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Abstract

The paper develops a $(2+2)$-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The formalism is two-dimensionally covariant, and leads to simple, geometrically transparent and tractable expressions for the Einstein field equations and the Einstein-Hilbert action, and it should find a variety of applications. It is applied here to elucidate the structure of the characteristic initial-value problem of general relativity.

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P. R. Brady, S. Droz, W. Israel, S. M. Morsink. 1995-10-19. Covariant double-null dynamics: $(2+2)$-splitting of the Einstein equations. https://doi.org/10.1088/0264-9381%2F13%2F8%2F015

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