Stability of charged black holes in de Sitter spacetimes proven.
problem Stability of charged black holes in de Sitter spacetimes.
method Global non-linear stability proof without symmetry assumptions, using initial value problem for Einstein-Maxwell equations.
result Exponential decay of perturbed KNdS black hole metrics and electromagnetic fields to KNdS family values.
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.
New black hole solutions found for specific conditions.
problem Finding unique black hole solutions under certain conditions.
method Non-linear stability of Kerr-Newman-de Sitter family, extension argument for Killing vector fields.
result Stationary solutions close to Reissner-Nordström-de Sitter are Kerr-Newman-de Sitter solutions for small angular momenta.
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.
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.
Study proves stability of slowly rotating Kerr black holes.
problem Stability of slowly rotating Kerr black holes.
method Linear stability analysis using wave map/DeTurck gauge, microlocal analysis, and non-elliptic Fredholm theory.
result Linearized perturbations decay at an inverse polynomial rate.
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.
Study on the interior of rotating vacuum black holes, proving stability of Cauchy horizon.
problem Stability of Cauchy horizon in rotating vacuum black holes.
method Maximal Cauchy evolution extension across non-trivial piece of Cauchy horizon.
result Continuous metric Cauchy horizon can be extended across a non-trivial piece of Cauchy horizon.
Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …
Proves stability of charged black holes with small charge.
problem Linear stability of Reissner-Nordström spacetime for small charge.
method Proves stability of Reissner-Nordström family of charged black holes using linearized Einstein-Maxwell equations and geodesic null foliations.
result Solutions decay to a linearized Kerr-Newman metric, proving stability.
Proves stability of gravitational instantons, proving operator positivity.
problem Stability of gravitational instantons.
method Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons.
result Teukolsky equation is a positive definite operator on Hermitian, non-self-dual gravitational instantons.
Classifies and analyzes the stability of black hole event horizon birth points using contact geometry.
problem Classifying and understanding the structural possibilities of black hole crease sets.
method Contact geometry approach, focusing on BigFronts and their Legendrian projections.
result Refined stability discussion of the event horizon birth component and identification of additional components.
Stability of extremal Reissner-Nordström black holes proven in spherical symmetry.
problem Stability of extremal Reissner-Nordström black holes in spherical symmetry.
method Proved nonlinear asymptotic stability through spherically symmetric characteristic data.
result Existence of a submanifold Mstab leading to stable solutions. 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…
Proves stability of Schwarzschild black holes without symmetry assumptions.
problem Stability of Schwarzschild black holes under general conditions.
method Teleologically normalised double null gauges, analysis of linear stability, and control of non-linearities.
result Proves non-linear asymptotic stability of Schwarzschild family as solutions to Einstein vacuum equations.
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.
Study on higher-dimensional black holes, focusing on retractions and scalar quasibound states.
problem Examining the physics of a five-dimensional non-extremal Reissner-Nordström black hole.
method Analyzing the line element and scalar field perturbations using polynomial conditions of Heun functions.
result Obtained analytical expressions for quasibound state frequencies and discussed system stability.
We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation whe…
Schwarzschild black hole stability proven using a new gauge.
problem Linear stability of Schwarzschild black holes to gravitational perturbations.
method Proved stability by imposing a generalised wave gauge.
result Uniform boundedness and polynomial decay of solutions.
Stability of Schwarzschild singularity in near-Schwarzschild black holes under perturbations.
problem Stability of the Schwarzschild singularity in near-Schwarzschild black holes.
method Energy methods and new approach to Einstein vacuum equations in axial symmetry.
result The solution displays asymptocially-velocity-term-dominated dynamics and approaches a different Kasner solution at each point of the singularity.
Abstract reviews geometric wave and Dirac equations on manifolds.
problem Analyzing geometric equations on manifolds.
method Well-posedness and stability for initial value problems, structure of equations on black-hole spacetimes, index theorem for hyperbolic Dirac operators, properties of Green-hyperbolic operators.
result Results on the structure of wave and Dirac equations on black-hole spacetimes, including the Kerr solution.
New data shows multiple black holes can form from modified vacuum data.
problem Formation of multiple black holes from modified vacuum data.
method Modified Brill-Lindquist metric, short-pulse framework, stability analysis, gluing method.
result Formation of multiple black holes in finite time under weak cosmic censorship.
We review our recent work on linear stability for scalar perturbations of Kerr spacetimes, that is to say, boundedness and decay properties for solutions of the scalar wave equation \Box_gψ = 0 on Kerr exterior backgrounds. We begin with the very slowly rotating case |a| \ll M, where first boundedness and then decay ha…
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…
Proves stability of Schwarzschild black holes, showing metric coefficients decay.
problem Linear stability of Schwarzschild black holes in vacuum Einstein equations.
method Linearized gravity, Hodge decomposition, gauge-invariant master quantities, decay estimates.
result Metric coefficients decay to linearized Kerr metric on exterior region.
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…
We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…
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 study some aspects of spherical symmetric dyonic non-supersymmetric black holes in 4dN=1 supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton…
Proof of reverse isoperimetric inequality for black holes.
problem Reverse isoperimetric inequality for black holes in Einstein gravity.
method Geometric-analytic approach.
result Reversal of the usual isoperimetric inequality is explained by curved backgrounds governed by Einstein's equations.
This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.
problem Understanding the black hole threshold in a moduli space of spherically symmetric spacetimes.
method Complete description and analysis of the black hole threshold in the moduli space M. result The black hole threshold is the extremal leaf of a C1 foliation of the moduli space, separating black hole solutions from non-collapsing solutions. 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…
Study bounds outer surfaces in small mass geometrostatic manifolds.
problem Bounding outer surfaces in geometrostatic manifolds with small ADM mass.
method Proving Intrinsic Flat Stability of the Positive Mass Theorem.
result Stability of the Positive Mass Theorem in geometrostatic manifolds with small ADM mass.
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.
2D twistor manifolds explain Teukolsky equations for rotating black holes.
problem Understanding the geometry of Teukolsky equations for rotating black holes.
method Using 2D twistor manifolds to explain the Teukolsky equations.
result All geometric structures can be understood by considering a 2D twistor manifold.
Researchers create black holes isometric to extremal Reissner-Nordström.
problem Third law of black hole thermodynamics.
method Novel Ck characteristic gluing procedure and scalar field pulses. result Definitive disproof of the third law of black hole thermodynamics.
Topology connects to black holes and wormholes.
problem Understanding topological changes in 3D space.
method Direct connection via surgery.
result New insights into black hole and wormhole formation.
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.
Scattering theory developed for linearised gravity near Schwarzschild black hole.
problem Linear stability of Schwarzschild spacetime and scattering of gravitational waves.
method Physical-space Chandrasekhar transformation and Teukolsky-Starobinsky correspondence.
result Construction of scattering theory for spin 2 Teukolsky equations.
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.
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.
Study of waves on Reissner-Nordström-AdS black holes, proving uniform boundedness and continuity.
problem Analyzing waves on black holes in AdS spacetimes, focusing on uniform boundedness and continuity.
method Initial data on a spacelike hypersurface, Dirichlet boundary conditions at infinity, proving uniform boundedness and continuity.
result Uniform boundedness and continuity of waves at the Cauchy horizon on Reissner-Nordström-AdS black holes.
RG-2 flow reveals horizons in noncompact black hole metrics.
problem Understanding the evolution of black hole metrics under RG-2 flow.
method Adapted proofs for asymptotically flat case, analyzed horizons and monotonicity of entanglement entropy.
result Entanglement entropy is monotonic under RG-2 flow, related to horizon appearance.
New black hole models with both null and spacelike singularities.
problem Understanding singularities in black hole spacetimes.
method Developed a new spacelike-characteristic gluing method to construct black hole spacetimes.
result First examples of black holes with coexisting null and spacelike singularities.
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentrici…
Deep neural network predicts black hole merger remnants with high accuracy.
problem Estimating the properties of black hole merger remnants.
method Trained on a dataset of binary black hole simulations, a deep neural network predicts mass and spin with high precision.
result The network predicts remnant black hole mass and spin with errors less than 0.04% and 0.3% respectively, and reduces errors in precessing cases to half.
Study proves inequality linking black hole properties and angular momentum.
problem Establishing a Penrose-type inequality for black holes with 3-sphere horizons.
method Analyzing biaxially symmetric, maximal, asymptotically flat initial data sets for the Einstein equations.
result Equality holds only for stationary Myers-Perry black holes.