Black-hole uniqueness theorems in Euclidean quantum gravity
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.
- Research Organization:
- Institute for Advanced Study, School of Natural Sciences, Princeton, New Jersey 08540
- OSTI ID:
- 5003895
- Journal Information:
- Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 22:8; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
BOUNDARY CONDITIONS
EINSTEIN FIELD EQUATIONS
EQUATIONS
EUCLIDEAN SPACE
FEYNMAN PATH INTEGRAL
FIELD EQUATIONS
FIELD THEORIES
INTEGRALS
KERR METRIC
MATHEMATICAL SPACE
METRICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RIEMANN SPACE
SCHWARZSCHILD RADIUS
SPACE