Extremal horizons stationary to the second order: new constraints

Abstract

We consider non-expanding shear free (NE-SF) null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes. A NE-SF null surface geometry consists of a degenerate metric tensor and a consistent torsion free covariant derivative. We derive the constraints implied by the existence of an embedding. The first constraint is well known as the near horizon geometry equation. The second constraint we find is new. The constraints lead to a complete characterization of those NE-SF null geometries that are embeddable in the extremal Kerr spacetime. Our results are also valid for spacetimes with a cosmological constant.

20 pages, a typo in Eq. (22) corrected

References in corpus (5)

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Cited by in corpus (3)

• Almost all extremal black holes in AdS are singular
• Isolated horizons of the Hopf bundle structure transversal to the null direction, the horizon equations and embeddability in NUT-like spacetimes
• Lie point symmetries of near-horizon geometry equation