Electrovacuum spacetime near an extreme horizon
arXiv:1809.08164 · doi:10.4310/ATMP.2019.v23.n7.a5
Abstract
We determine all infinitesimal transverse deformations of extreme horizons in Einstein-Maxwell theory that preserve axisymmetry. In particular, we show that the general static transverse deformation of the AdS(2) X S(2) near-horizon geometry is a two-parameter family, which contains the known extreme charged, accelerating, static black hole solution held in equilibrium by an external electric or magnetic field (Ernst solution) and a special case of the extreme Kerr-Newman-Melvin solution. More generally, we find a three-parameter family of deformations of the extreme Kerr-Newman horizon, which contains the extreme Kerr-Newman-Melvin solution and a rotating generalisation of the Ernst solution. We also consider vacuum gravity with a cosmological constant and prove uniqueness of axisymmetric transverse deformations of the extreme Kerr-AdS horizon. Finally, we completely classify transverse deformations of extreme horizons in three-dimensional Einstein-Maxwell theory with a negative cosmological constant.
36 pages
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- Horizons as boundary conditions in spherical symmetry
- Uniqueness of extremal charged black holes in de Sitter
- Rigidity of the extremal Kerr-Newman horizon
- Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes