TypeN vacuum spacetimes as special functions in ?^{2}
Abstract
The members of one explicit class of functions in ?^{2} are identified with the geodetic shearfree null congruences in Minkowski's spacetime. Members of a second explicit class are identified with the typeN vacuum spacetimes with twistfree rays. These two classes are special subclasses from a larger class of functions associated with the typeN spacetimes. 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 CauchyRiemann equation for an antiholomorphic function on the 3surface whereu (ϕ, ζ,bar ζ ) has real values.
 Publication:

General Relativity and Gravitation
 Pub Date:
 October 1977
 DOI:
 10.1007/BF00759589
 Bibcode:
 1977GReGr...8..855S