Abstract
All axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological 2-sphere were derived. The regularity conditions preventing cone singularity at the poles were accounted for. The one-to-one correspondence of the solutions with the extremal horizons in the Kerr–(anti–)de Sitter spacetimes was found. A solution corresponding to the triply degenerate horizon was identified and characterized. The solutions were also identified among the solutions to the Petrov type D equation.
- Received 19 February 2021
- Accepted 2 April 2021
DOI:https://doi.org/10.1103/PhysRevD.103.104004
© 2021 American Physical Society
Physics Subject Headings (PhySH)
Gravitation, Cosmology & Astrophysics