Global embedding of the Kerr black hole event horizon into hyperbolic 3-space
- D.A.M.T.P., Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
- Departamento de Fisica e Centro de Fisica do Porto, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto (Portugal)
An explicit global and unique isometric embedding into hyperbolic 3-space, H{sup 3}, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H{sup 3} of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H{sup 3}, for arbitrary values of the angular momentum. For this example, considering a quotient of H{sup 3} by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding that cannot be made global.
- OSTI ID:
- 21322473
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 4; Other Information: DOI: 10.1103/PhysRevD.80.044014; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Embedding of the Kerr-Newman black hole surface in Euclidean space
Statistical Entropy of Four-Dimensional Rotating Black Holes from Near-Horizon Geometry