Staticity and uniqueness of multiple black hole solutions of sigma -models
- 1 April 1993
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 10 (4) , 791-799
- https://doi.org/10.1088/0264-9381/10/4/014
Abstract
The author proves the staticity and no-hair conjectures for self-gravitating nonlinear sigma -models with Riemannian target manifolds. The author first demonstrates that any self-coupled, stationary scalar mapping ( sigma -model) from a strictly stationary domain of outer communications with nonrotating horizon to a Riemannian manifold has to be static. Applying the positive mass theorem, the author subsequently shows that the exterior Schwarzschild geometry is the only maximally extended, static, asymptotically flat solution of the coupled Einstein- sigma -model equations with regular (but not necessarily connected) horizon.Keywords
This publication has 37 references indexed in Scilit:
- Bunting identity and Mazur identity for non-linear elliptic systems including the black hole equilibrium problemCommunications in Mathematical Physics, 1985
- Proof of uniqueness of the Kerr-Newman black hole solutionJournal of Physics A: General Physics, 1982
- Uniqueness of the Kerr Black HolePhysical Review Letters, 1975
- Classification of black holes with electromagnetic fieldsPhysical Review D, 1974
- Black holes in static electrovac space-timesGeneral Relativity and Gravitation, 1974
- Elastic perturbation theory in General Relativity and a variation principle for a rotating solid starCommunications in Mathematical Physics, 1973
- Black holes in static vacuum space-timesGeneral Relativity and Gravitation, 1973
- Axisymmetric Black Hole Has Only Two Degrees of FreedomPhysical Review Letters, 1971
- Event horizons in static electrovac space-timesCommunications in Mathematical Physics, 1968
- Event Horizons in Static Vacuum Space-TimesPhysical Review B, 1967