Degenerate Killing Horizons Research Articles

Multiple Killing horizons and near horizon geometries

Near horizon geometries with multiply degenerate Killing horizons are considered, and their degenerate Killing vector fields identified. We prove that they all arise from hypersurface-orthogonal Killing vectors of any cut of with the inherited metric—cuts are spacelike co-dimension two submanifolds contained in . For each of these Killing vectors on a given cut, there are three different possibilities for the near horizon metric which are presented explicitly. The structure of the metric for near horizon geometries with multiple Killing horizons of order is thereby completely determined, and in particular we prove that the cuts on must be warped products with maximally symmetric fibers (ergo of constant curvature). The question whether multiple degenerate Killing horizons may lead to inequivalent near horizon geometries by using different degenerate Killings is addressed, and answered on the negative: all near horizon geometries built from a given multiple degenerate Killing horizon (using different degenerate Killings) are locally isometric.

Linear waves on constant radius limits of cosmological black hole spacetimes

In this paper we consider the Klein-Gordon equation on spherically symmetric background spacetimes with a constant area radius. The spacetimes under consideration are Nariai and Plebanski-Hacyan, and can be considered constant radius limits of Reissner-Nordstrom-de Sitter spacetimes. We prove boundedness in the case of a non-negative Klein Gordon mass and decay unless the mass is zero. In the latter case we prove decay of solutions that are supported on all harmonic modes with angular momentum l greater or equal to 1. We show that the l=0 modes of solutions to the massless Klein-Gordon equation do not decay. They are subject to conservation laws along degenerate Killing horizons. We apply the estimates in Nariai to give decay of solutions to the massive Klein-Gordon equation on an n-dimensional de Sitter background, using only the vector field method and with no restrictions on the positive Klein-Gordon mass.

Asymptotically flat multiblack lenses

We present an asymptotically flat and stationary multi-black lens solution with bi-axisymmetry of $U(1)\times U(1)$ as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of $L(n,1)=S^3/{\mathbb Z_n}$ as well as a sphere $S^3$. Moreover, we show that in contrast to the higher dimensional Majumdar-Papapertrou multi-black hole and multi-BMPV black hole spacetimes, the metric is smooth on each horizon even if the horizon topology is spherical.

Classification of Near-Horizon Geometries of Extremal Black Holes.

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

On higher dimensional black holes with Abelian isometry group

We consider (n+1)-dimensional, stationary, asymptotically flat, or Kaluza–Klein asymptotically flat black holes with an Abelian s-dimensional subgroup of the isometry group satisfying an orthogonal integrability condition. Under suitable regularity conditions, we prove that the area of the group orbits is positive on the domain of outer communications ⟨⟨Mext⟩⟩, vanishing only on the boundary ∂⟨⟨Mext⟩⟩ and on the “symmetry axis” A. We further show that the orbits of the connected component of the isometry group are timelike throughout the domain of outer communications. Those results provide a starting point for the classification of such black holes. Finally, we show nonexistence of zeros of static Killing vectors on degenerate Killing horizons, as needed for the generalization of the static no-hair theorem to higher dimensions.

On the existence of Kundt's metrics and degenerate (or extremal) Killing horizons

It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional spacelike sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus g ⩾ 2 is excluded by vacuum Einstein equations. The so-called basic equation (resulting from Einstein equations) is examined. This is a nonlinear PDE for an unknown covector field and an unknown Riemannian structure on the two-dimensional manifold. It implies several important results derived in this paper. It arises not only for Kundt's class but also for degenerate Killing horizons and vacuum degenerate isolated horizons.

Global structure of the Zipoy–Voorhees–Weyl spacetime and the δ = 2 Tomimatsu–Sato spacetime

We investigate the structure of the ZVW (Zipoy–Voorhees–Weyl) spacetime, which is a Weyl solution described by the Zipoy–Voorhees metric, and the δ = 2 Tomimatsu–Sato spacetime. We show that the singularity of the ZVW spacetime, which is represented by a segment ρ = 0, − σ < z < σ in the Weyl coordinates, is geometrically point-like for δ < 0, string-like for 0 < δ < 1 and ring-like for δ > 1. These singularities are always naked and have positive Komar masses for δ > 0. Thus, they provide a non-trivial example of naked singularities with positive mass. We further show that the ZVW spacetime has a degenerate Killing horizon with a ring singularity at the equatorial plane for δ = 2, 3 and δ ⩾ 4. We also show that the δ = 2 Tomimatsu–Sato spacetime has a degenerate horizon with two components, in contrast to the general belief that the Tomimatsu–Sato solutions with even δ do not have horizons.

Note on degenerate Killing horizons

Manifestly regular double-null coordinates are constructed for degenerate Killing horizons. It is shown that the red-shift and stability properties of degenerate horizons differ from those of nondegenerate horizons.