Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry.

Details Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry. Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry.

May 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gregr..18..511p&link_type=abstract

General Relativity and Gravitation, Volume 18, Issue 5, pp.511-530

Computer Science

3

Gravitation Theory:Space-Time

Scientific paper

The conjecture is proved that stationary vacuum space-times having a conformally flat three-space are axially symmetric. The proof uses the Ernst potential and the complex conjugate potential as independent coordinates. Two field equations: a combination of the Einstein equations and an integrability condition are algebraic in one of the field variables. Their coefficients, computed by employing a REDUCE program, separately vanish unless axial symmetry holds. Solution of the coefficient equations yields the proof of axial symmetry. Certain special classes of metrics must be excluded from the discussion. The axial symmetry of these exceptional classes has been proved in I.

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