Mathematics – Complex Variables
Scientific paper
Apr 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..11.2063b&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 11, Apr. 15, 1975, p. 2063-2071.
Mathematics
Complex Variables
1
Astronomical Models, Field Theory (Physics), Space-Time Functions, Symmetry, Vacuum, Asymptotic Methods, Complex Variables, Radiative Transfer, Vector Analysis
Scientific paper
Using the formalism of Bondi et al. (1962), it is shown that in an axisymmetric asymptotically flat vacuum space-time, the existence of another isometry causes all possible solutions to be nonradiative. The formalism is briefly presented, Killing's equations are written in Bondi's coordinates, and the almost general case of an arbitrary isometry is analyzed. Numerous special cases are also analyzed, and a class of solutions is obtained which has the isometry anywhere in the plane spanned by two null real vectors. Solutions are reviewed which have the isometry in the real plane spanned by two null complex vectors, and the negative result is analyzed for Killing vectors with orbits in the two real null directions. The analysis of all the different cases demonstrates unambiguously that if a Killing vector field, which is linearly independent of the axial symmetry, exists in a space-time, then that space-time must be nonradiative.
Berezdivin R.
Herrera Luis
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