The Uniqueness Theorem for Rotating Black Hole Solutions of Self-gravitating Harmonic Mappings
نویسنده
چکیده
We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of selfgravitating harmonic mappings.
منابع مشابه
Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black hole solutions to the stationary Einstein equations has increased in an unexpected way during the last decade. In particular, it has turned out that not all black hole equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black hole space-times ceas...
متن کاملNo-hair Theorems and Black Holes with Hair
The critical steps leading to the uniqueness theorem for the Kerr-Newman metric are examined in the light of the new black hole solutions with Yang-Mills and scalar hair. Various methods – including scaling techniques, arguments based on energy conditions, conformal transformations and divergence identities – are reviewed, and their range of application to selfgravitating scalar and non-Abelian...
متن کاملRotating Circular Strings, and Infinite Non-Uniqueness of Black Rings
We present new self-gravitating solutions in five dimensions that describe circular strings, i.e., rings, electrically coupled to a two-form potential (as e.g., fundamental strings do), or to a dual magnetic one-form. The rings are prevented from collapsing by rotation, and they create a field analogous to a dipole, with no net charge measured at infinity. They can have a regular horizon, and w...
متن کاملN - Black Hole Stationary Andaxially Symmetric Solutions Ofthe Einstein - Maxwell
It is well-known that the Einstein-Maxwell equations reduce in the stationary and axially symmetric case to an axially symmetric harmonic map with prescribed singularities ': R 3 n ! H 2 C , where is a subset of the axis of symmetry, and H 2 C is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities ': R n n...
متن کاملN-black Hole Stationary and Axially Symmetric Solutions of the Einstein/maxwell Equations
The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \ Σ → H2C , where Σ is a subset of the axis of symmetry, and H2C is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is a submanifold of R of co...
متن کامل