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Related papers: Intrinsic rigidity of extremal horizons

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Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…

General Relativity and Quantum Cosmology · Physics 2011-07-19 Abhay Ashtekar , Christopher Beetle , Jerzy Lewandowski

We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our…

Differential Geometry · Mathematics 2026-02-11 Hiroyasu Satoh , Hemangi Madhusudan Shah

We extend the following result of Cochran ``A closed $m$-quasi Einstein manifold ($M,g,X$) with $m \ne -2$ has constant scalar curvature if and only if $X$ is Killing" covering the missing accidental case $m=-2$ and generalize it showing…

Differential Geometry · Mathematics 2025-05-15 Ramesh Sharma

The near-horizon limit of the extremal (weakly) isolated horizon is obtained under the Bondi-like coordinates. For the vacuum case, explicit coordinate transformation relating the near-horizon metric under the Bondi-like coordinates and the…

High Energy Physics - Theory · Physics 2009-09-02 Xiao-Ning Wu , Yu Tian

We formulate conditions on the geometry of a non-expanding horizon $\Delta$ which are sufficient for the space-time metric to coincide on $\Delta$ with the Kerr metric. We introduce an invariant which can be used as a measure of how…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Jerzy Lewandowski , Tomasz Pawlowski

We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr--Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Jun-ichirou Koga

Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed…

General Relativity and Quantum Cosmology · Physics 2017-12-06 Nicola Franchini , Mehdi Saravani , Thomas P. Sotiriou

For arbitrary static space-times, it is shown that an equilibrium between a Killing horizon and matter is only possible for some discrete values of the parameter $w = p_1/\rho$, where $\rho$ is the density and $p_1$ is pressure in the…

General Relativity and Quantum Cosmology · Physics 2010-04-14 K. A. Bronnikov , O. B. Zaslavskii

We prove a black hole rigidity result for slowly rotating stationary solutions of the Einstein vacuum equations. More precisely, we prove that the domain of outer communications of a regular stationary vacuum is isometric to the domain of…

General Relativity and Quantum Cosmology · Physics 2015-01-14 S. Alexakis , A. D. Ionescu , S. Klainerman

In this paper, we first show that the definition of the universal horizons studied recently in the khrononmetric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply…

General Relativity and Quantum Cosmology · Physics 2015-01-05 Kai Lin , Elcio Abdalla , Rong-Gen Cai , Anzhong Wang

Smooth spacetimes with a compact Cauchy horizon ruled by closed null geodesics are considered. The compact Cauchy horizon is assumed to be non-degenerate. Then, supporting the validity of Penrose's strong cosmic censor hypothesis, the…

General Relativity and Quantum Cosmology · Physics 2017-08-23 István Rácz

In this paper, we study the existence of universal horizons in a given static spacetime, and find that the test khronon field can be solved explicitly when its velocity becomes infinitely large, at which point the universal horizon…

General Relativity and Quantum Cosmology · Physics 2015-03-05 Kai Lin , O. Goldoni , M. F. da Silva , Anzhong Wang

Static solutions of the Einstein-Yang-Mills-Higgs system containing extreme black holes are studied. The field equations imply strong restrictions on boundary values of all fields at the horizon. If the Yang-Mills radial electric field $E$…

General Relativity and Quantum Cosmology · Physics 2010-04-06 J. Bicak , C. Cris , P. Hajicek , A. Higuchi

Spherically, plane, or hyperbolically symmetric spacetimes with an additional hypersurface orthogonal Killing vector are often called ``static'' spacetimes even if they contain regions where the Killing vector is non-timelike. It seems to…

General Relativity and Quantum Cosmology · Physics 2021-11-02 Hideki Maeda

The uniqueness and rigidity of black holes remain central themes in gravitational research. In this work, we investigate the construction of all extremal black hole solutions to the Einstein equation for a given near-horizon geometry,…

High Energy Physics - Theory · Physics 2026-02-06 Jan Gutowski , Chettha Saelim , Martin Wolf

Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $\xi^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$:…

General Relativity and Quantum Cosmology · Physics 2025-09-25 Abhay Ashtekar , Badri Krishnan

In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…

General Relativity and Quantum Cosmology · Physics 2014-12-16 Rodrigo Maier

We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a…

High Energy Physics - Theory · Physics 2015-09-23 Dietmar Klemm , Masato Nozawa

An almost K\"ahler structure is {\it extremal} if the Hermitian scalar curvature is a Killing potential [29]. When the almost complex structure is integrable it coincides with extremal K\"ahler metric in the sense of Calabi [8]. We observe…

Differential Geometry · Mathematics 2018-11-15 Eveline Legendre

We prove that every conformal vector field on the complex hyperbolic space $\mathbb{C}H^n$ is Killing for all $n\ge 2$. Although this rigidity is classically known, our proof is entirely different in nature: it is local, analytic, and fully…

Differential Geometry · Mathematics 2026-02-23 Hiroyasu Satoh , Hemangi Madhusudan Shah