Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
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48 results for “extreme Kerr black hole”
Proves uniqueness of non-extremal Kerr-Newman black holes under small perturbations.
problem Uniqueness of non-extremal Kerr-Newman black holes under small perturbations.
method Perturbative analysis using Mars-Simon type tensors.
result Proves that a space-time close to the Kerr-Newman family must be one of the Kerr-Newman solutions.
Researchers compute quasi-local mass of Kerr black hole horizon.
problem Computing the quasi-local mass of Kerr black hole horizons.
method Isometric embedding of Kerr black hole horizon in hyperbolic space.
result Quasi-local mass varies with Kerr black hole spin parameter.
Study of harmonic maps with extreme Kerr-like singularities.
problem Analyzing harmonic maps with specific singularities.
method Asymptotic analysis of harmonic maps from 3D Euclidean space to hyperbolic plane.
result Existence and classification of tangent harmonic maps at extreme black hole horizons.
The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and…
Achieved all-orders worldline action for Kerr black hole.
problem Calculating effective action for Kerr black hole.
method Twistor particle theory.
result All-orders worldline effective action for Kerr black hole.
Effective action for Kerr-Newman black hole found in twistor theory.
problem Effective action for Kerr-Newman black hole.
method Twistor particle theory to achieve all-orders worldline effective action.
result Exact hidden symmetries identified in self-dual backgrounds.
Constructs solutions of Einstein equations for black holes gluing along timelike geodesics.
problem Constructing solutions of Einstein equations for black holes gluing along timelike geodesics.
method Constructs solutions of the Einstein equations describing a mass Kerr black hole traveling along a timelike geodesic .
result Constructs true solutions of the Einstein equations for black holes gluing along timelike geodesics.
Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.
problem Formation of Kerr black holes and Penrose inequalities.
method Combining gravitational-collapse and Kerr stability results with new coordinate changes and elliptic arguments.
result Proves dynamical and spacetime Penrose inequalities in black hole formation spacetimes.
This work proves Kerr black holes are dynamically stable under certain perturbations.
problem Dynamical stability of Kerr black holes under axially symmetric perturbations.
method Dimensional reduction to 2+1 Einstein-wave map system, construction of positive-definite energy functional, proving boundary terms vanish.
result Strictly conserved positive energy for axially symmetric linear perturbations of Kerr black holes.
A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous E…
New quasi-Einstein metrics found on a sphere.
problem Finding quasi-Einstein metrics on a sphere.
method Constructing axi-symmetric non-gradient -quasi-Einstein structures using hypergeometric functions.
result Found new regular metrics on a two-sphere, including the extreme Kerr black hole horizon.
The paper proves the existence of a horizon for certain spacetimes.
problem Existence of horizons in asymptotically stationary spacetimes.
method General unstable manifold theorem for perturbations of flows.
result Existence of a unique null hypersurface asymptotic to a horizon.
Researchers found a way to measure energy in black hole perturbations.
problem Lack of positive-definite and conserved energy in black hole stability.
method Dimensional reduction and construction of a positive-definite energy functional.
result Conserved Hamiltonian energy for axially symmetric perturbations of Kerr black holes.
Researchers extend microlocal analysis across event horizons of rotating black holes.
problem Incomplete microlocal theory of fields across black hole event horizons.
method Extended microlocal theory for extremal rotating black holes, showing null covectors form an involutive double characteristic manifold.
result Mathematical basis for asymptotic oscillatory solutions near event horizons.
Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
problem Understanding the asymptotic behavior of black hole geometries.
method Used hidden symmetry and conformal geometry technology to find necessary conditions.
result Necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in…
We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics …
Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.
problem Global existence and boundedness for quasilinear wave equations on Kerr black holes.
method Combines linear inhomogeneous estimates on Kerr backgrounds and tailored physical space currents.
result Global existence, boundedness and decay for small data solutions to quasilinear wave equations on Kerr black holes.
We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…
New construction of self-dual black holes using quadrics.
problem Hidden features of self-dual black holes obscured by twistor theory.
method Holomorphic quadrics in dual twistor space.
result Directly encoded geometry of self-dual black holes in quadrics.
Recently it was shown that the area A and the angular momentum J of any apparent horizon on a maximal, axisymmetric and asymptotically flat Cauchy hyper-surface of a vacuum space-time satisfy necessarily the universal inequality A >= 8 pi |J|. We show here that the equality A=8 pi |J| is never attained. As equality is …
We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordström-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the non-linear stability of the Kerr-Newman-de Sitter family of black holes for small angular…
New approach simplifies proof of wave equations on black holes.
problem Global existence and decay for semilinear wave equations on extremal Reissner-Nordström black holes.
method Develops a new approach based on weaker estimates, avoiding near-horizon sharp estimates.
result Simpler and more streamlined proof without requiring near-horizon sharp estimates.
We show that a stationary asymptotically flat electro-vacuum solution of Einstein's equations that is everywhere locally "almost isometric" to a Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular this implies that the assumption of a single event horizon in Alexa…
Establishes inequality for multiple black holes, proving mass lower bound.
problem Proving mass-angular momentum inequality for multiple black holes.
method Novel flow of singular harmonic maps with hyperbolic plane target.
result Mass lower bound for ADM mass and angular momentum.
These lecture notes, based on a course given at the Zurich Clay Summer School (June 23-July 18, 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this problem stems from its relationship to the non-linear stability of the black hole spa…
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …
Stability of black holes proven in full subextremal range with positive cosmological constant.
problem Stability of Kerr-de Sitter black holes in the full subextremal range.
method Similar to previous proof in slowly rotating case, with implementation of constraint damping and verification of subprincipal symbol condition.
result Stability of Kerr-de Sitter black holes proven in the full subextremal range.
The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a …
Constructs many black hole spacetimes in de Sitter space.
problem Creating well-controlled many black hole spacetimes in de Sitter space.
method Gluing Schwarzschild-de Sitter or Kerr-de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions.
result Solves the Einstein equation directly for the metric, given scattering data at the future conformal boundary.
We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This resu…
We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase sp…
The paper explores Kähler structures of Taub-NUT and Kerr spaces.
problem Understanding Kähler properties of gravitational instantons and black holes.
method Analyzing Euclidean Taub-NUT and Kerr metrics using alternative coframes and conformal scaling.
result Euclidean Taub-NUT and Kerr metrics exhibit hyper-Kähler and globally conformally Kähler properties, respectively.
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…
Formally constructs metrics near timelike geodesics in vacuum spacetimes.
problem Constructing metrics near timelike geodesics in spacetimes.
method Constructs a family of metrics depending on a small parameter ε, solving the Einstein vacuum equations modulo O(ε^∞).
result The rescalings near the geodesic tend to a fixed subextremal Kerr metric.
Study gluing event horizons of Minkowski and Schwarzschild spacetimes.
problem Gluing event horizons of different spacetimes.
method Nonperturbative, gluing results from Aretakis-Czimek-Rodnianski and Christodoulou's short pulse method.
result Construct examples of vacuum gravitational collapse to very slowly rotating Kerr black holes.
We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term …
In this paper, we provide an elementary, unified treatment of two distinct blue-shift instabilities for the scalar wave equation on a fixed Kerr black hole background: the celebrated blue-shift at the Cauchy horizon (familiar from the strong cosmic censorship conjecture) and the time-reversed red-shift at the event hor…
Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holesgr-qc
Global existence and decay for quasilinear wave equations on various spacetimes, including Kerr black holes.
problem Global existence and decay for quasilinear wave equations on asymptotically flat spacetimes.
method Dyadically localised nature and direct use of a blackbox linear inhomogeneous energy estimate on exactly stationary metrics.
result Global existence and decay for small-data solutions to quasilinear wave equations on a wide variety of spacetime backgrounds, including Kerr black holes.
Uniqueness theorem for extremal charged black holes in de Sitter space.
problem Proving uniqueness of extremal charged black holes in de Sitter space.
method Analyzing Einstein-Maxwell theory with a positive cosmological constant.
result Local isometry to extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry.
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the exp…
This paper proves a canonical foliation on null infinity for Kerr-like black holes.
problem Establishing well-defined physical quantities on null infinity for Kerr-like black holes.
method Existence and uniqueness results for GCM spheres by Klainerman-Szeftel.
result Existence of a canonical foliation on future null infinity with well-defined physical quantities.
Adds charged black holes to de Sitter space.
problem Gluing charged black holes into de Sitter space.
method Extends Hintz's result to Einstein-Maxwell system with positive cosmological constant, using Reissner-Nordström or Kerr--Newman--de Sitter black holes.
result Determines conditions for gluing black holes into de Sitter space.
New memory effect discovered in gravitational wave behavior.
problem Understanding gravitational wave behavior in spacetimes with angular momentum.
method Mathematical analysis of Minkowski spacetime and Kerr black holes.
result Angular momentum memory effect observed at future null infinity.
Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energygr-qc
Based on the Hamiltonian dimensional reduction of axially symmetric, Ricci-flat Lorentzian spacetimes to a Einstein-wave map system with the (negatively curved) hyperbolic 2-plane target, we construct a positive-definite, (spacetime) gauge-invariant energy functional for linear axially symmetric perturbatio…
Extreme black holes with $\SU(2)$ symmetry have a specific near horizon geometry.
problem Understanding the near horizon geometry of extreme black holes with $\SU(2)$ symmetry.
method Analyzing the near horizon geometry of 5D extreme black holes with $\SU(2)$ symmetry.
result The near horizon geometry of these black holes must be that of a Berger sphere.
We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the…