Black-hole uniqueness theorems in Euclidean quantum gravity

Details Black-hole uniqueness theorems in Euclidean quantum gravity Black-hole uniqueness theorems in Euclidean quantum gravity

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980phrvd..22.1837l&link_type=abstract

Physical Review D (Particles and Fields), Volume 22, Issue 8, 15 October 1980, pp.1837-1847

Physics

4

Scientific paper

The Euclidean section of the classical Lorentzian black-hole solutions has been used in approximating the functional integral in the Euclidean path-integral approach to quantum gravity. In this paper the claim that classical black-hole uniqueness theorems apply to the Euclidean section is disproved. In particular, it is shown that although a Euclidean version of Israel's theorem does provide a type of uniqueness theorem for the Euclidean Schwarzschild solution, a Euclidean version of Robinson's theorem does not allow one to form conclusions about the uniqueness of the Euclidean Kerr solution. Despite the failure of uniqueness theorems, "no-hair" theorems are shown to exist. Implications are discussed. A precise mathematical statement of the Euclidean black-hole uniqueness conjecture is made and the proof left as an unsolved problem in Riemannian geometry.

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