Uniqueness of the Kerr black hole

Details Uniqueness of the Kerr black hole Uniqueness of the Kerr black hole

Apr 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvl..34..905r&link_type=abstract

Physical Review Letters, vol. 34, Apr. 7, 1975, p. 905, 906.

Astronomy and Astrophysics

Astronomy

254

Astronomical Models, Black Holes (Astronomy), Einstein Equations, Uniqueness Theorem, Metric Space, Relativity, Space-Time Functions, Stellar Evolution, Vacuum

Scientific paper

The family of Kerr solutions, where the absolute value of the angular momentum is less than the gravitational mass, is shown to be the unique pseudostationary family of black hole solutions of the Einstein vacuum field equations when the event horizon is assumed to be nondegenerate. The scalar of twist potential and the scalar component of the four-dimensional metric which together uniquely determine the four-dimensional geometry for each possible black hole exterior are introduced. Calculations demonstrate that as long as these scalars satisfy certain conditions on the orthogonally intersecting components of the two-dimensional manifold boundary, regularity of the four-dimensional geometry on the axisymmetry axis and horizon results.

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