ON THE CHARACTERISTIC INITIAL VALUE PROBLEM IN GRAVITATIONAL THEORY
The problem of determining a solution of the Einstein field equations for the gravitational field from data set on a pair of intersecting characteristic (that is, null) hypersurfaces and on their intersection SIGMA is considered, It is shown that by giving the conformal inner metric of each hypersurface, the inner geometry of EPSILON , the two mean extrinsic curvatures of SIGMA , and one additional extrinsic quantity for SIGMA , a solution in a space-time region is completely determined. In a suitable coordinate system, giving the above data amounts to giving four functions of three variables, four functions of two variables, and one function of one variable; all these can be given without any constraints. In a given space-time with given SIGMA the functions are almost, but not entirely, known functions of their arguments. All the derivations and discussions are applicable only in a sufficiently small four- dimensional region. (auth)
- Research Organization:
- U.S. Army Signal Research and Development Lab., Fort Monmouth, N.J.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-002439
- OSTI ID:
- 4760295
- Journal Information:
- J. Math. Phys., Journal Name: J. Math. Phys. Vol. Vol: 3
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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