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 |