Related papers: Rigidity of the extremal Kerr-Newman horizon
We prove that the intrinsic geometry of compact cross-sections of any vacuum extremal horizon must admit a Killing vector field. If the cross-sections are two-dimensional spheres, this implies that the most general solution is the extremal…
When Gaussian null coordinates are adapted to a Killing horizon, the near-horizon limit is defined by a coordinate rescaling and then by taking the regulator parameter $\varepsilon$ to be small, as a way of zooming into the horizon…
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…
We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing…
We consider stationary extreme black hole solutions to the Einstein-Yang-Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon…
We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon…
We prove a uniqueness theorem for the charged Nariai black holes and ultracold black holes in four dimensions. In particular, we show that an analytic solution to four-dimensional Einstein-Maxwell theory with a positive cosmological…
A new proof of the uniqueness of the Kerr-Newman black hole solutions amongst asymptotically flat, stationary and axisymmetric electro-vacuum spacetimes surrounding a connected Killing horizon is given by means of an explicit construction…
We study some geometric properties of Killing horizons in 4-dimensional stationary and axisymmetric space-times with electromagnetic field and cosmological constant. Using a $(1+1+2)$ space-time split, we construct relations between the…
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…
We study non-degenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d>=4) static space-times. Using…
We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…
Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original…
Extremal horizons satisfy an equation induced by the Einstein vacuum equations that determines the shape of the horizon and the manner in which it rotates (the EEH equation). Until recently, however, the classification of solutions required…
We consider the near-horizon geometries of extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry…
It has often been suggested (especially by Carlip) that spacetime symmetries in the neighborhood of a black hole horizon may be relevant to a statistical understanding of the Bekenstein-Hawking entropy. A prime candidate for this type of…
We examine the linearized equations around extremal Kerr horizon and give some arguments towards stability of the horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry.
We show that the gravitational phase space for the near-horizon region of a bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal symmetry algebra with central charges proportional to the area. This extends the…
We discuss various properties of rotating Killing horizons in generic $F(R)$ theories of gravity in dimension four for spacetimes endowed with two commuting Killing vector fields. Assuming there is no curvature singularity anywhere on or…
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…