TypeN vacuum space-times as special functions in ?2

Details TypeN vacuum space-times as special functions in ?2 TypeN vacuum space-times as special functions in ?2

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..855s&link_type=abstract

General Relativity and Gravitation, Volume 8, Issue 10, pp.855-863

Physics

3

Scientific paper

The members of one explicit class of functions in ?2 are identified with the geodetic shear-free null congruences in Minkowski's space-time. Members of a second explicit class are identified with the type-N vacuum space-times with twist-free rays. These two classes are special subclasses from a larger class of functions associated with the type-N space-times. This larger class is characterized in the following way: Ifϕ andζ are holomorphic variables in ?2, the nu (ϕ, ζ,bar ζ ), a function holomorphic inϕ, belongs to the class provided the functionpartial _{ζ } partial _{ζ } ∂ ϕ u/∂ ϕ u satisfies the tangential Cauchy-Riemann equation for an antiholomorphic function on the 3-surface whereu (ϕ, ζ,bar ζ ) has real values.

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