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A simple example of type-{\rm [N]} \otimes {\rm [N]} {\cal HH} -spaces admitting twisting null geodesic congruence

Adam Chudecki1 and Maciej Przanowski2

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Expanding {\cal HH} -spaces with cosmological constant of the type [deg] otimes [deg] are considered. We find the expanding hyperheavenly equation describing such spaces and then we specify this equation to the case of the type [N] otimes [N]. An example of the solution of this last equation leading to the type-[N] otimes [N] {\cal HH} -space (with vanishing cosmological constant) admitting twisting null geodesic congruence is presented and the respective metric is explicitly given.


PACS

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

02.40.Tt Complex manifolds

98.80.Jk Mathematical and relativistic aspects of cosmology

MSC

32Qxx Complex manifolds

83F05 Cosmology

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 5 (7 March 2008)

Received 21 November 2007, in final form 14 January 2008

Published 15 February 2008



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