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Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations. (English) Zbl 0701.35149

It is shown that the characteristic initial value problem for a hyperbolic system can often be reduced to the Cauchy problem. This result is then applied to prove the existence and uniqueness of solutions to the Einstein equations in vacuum or with a perfect fluid source for given initial data on two transversely intersecting null hypersurfaces.
Reviewer: A.D.Rendall

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
35L45 Initial value problems for first-order hyperbolic systems
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