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

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

1995-10-19

arxiv.org/abs/gr-qc/9510040v1

Class.Quant.Grav. 13 (1996) 2211-2230

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, latex, one figure in a separate file

Scientific paper

10.1088/0264-9381/13/8/015

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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