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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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…
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 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.
The moduli space of dynamical spherically symmetric black hole spacetimes and the extremal thresholdgr-qc
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 .
result The black hole threshold is the extremal leaf of a 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…
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.
Introduces holed cone structures to generalize cone structures on 3-manifolds.
problem Generalizing cone structures to 3-manifolds with irreducible holonomy representations.
method Introduces holed cone structures and considers their deformation space.
result The deformation space of holed cone structures is a covering space of the character variety.
Researchers create black holes isometric to extremal Reissner-Nordström.
problem Third law of black hole thermodynamics.
method Novel characteristic gluing procedure and scalar field pulses.
result Definitive disproof of the third law of black hole thermodynamics.
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.
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.
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.
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.
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.
A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking'…
New concept of k-holes in simple drawings and convex drawings.
problem Investigate holes in convex and simple drawings.
method Structural investigation of pseudolinear subdrawings in convex drawings.
result Existence of empty 4-cycles in every simple drawing of K_n.
Proves no-hair theorem for certain vacuum black holes.
problem No-hair theorem for stationary vacuum black holes.
method Proof of no-hair theorem, definition of surface gravity and angular velocity, analysis of near-horizon geometries.
result Completion of no-hair theorem proof for specified black holes.
Warped-product black hole spacetimes are -inextendible.
problem Future -inextendibility of warped-product black hole spacetimes
method Adapting Sbierski's proof for a broad class of warped-product black hole spacetimes
result Future -inextendibility established for spacetimes with a static exterior region
The paper proves extremal black holes form at a critical point of gravitational collapse.
problem Formation of extremal black holes in gravitational collapse.
method Constructing smooth families of spherically symmetric solutions to the Einstein-Maxwell-Vlasov system.
result Extremal Reissner-Nordström black holes form at the critical collapse threshold.
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…
This paper explores charged black holes in 3+1 dimensions, finding limitations on their existence.
problem Classifying charged electrostatic black holes in arbitrary topology.
method Comparison geometry techniques.
result Charged Schwarzschild black holes are possible, but not Boosts or Myers-Korotkin-Nicolai solutions.
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.
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.
We show that if S is a finite type orientable surface of negative Euler characteristic which is not the 3-holed sphere, 4-holed sphere or 1-holed torus, then the ending lamination space of S is connected, locally path connected and cyclic.
Theorem proves topological censorship for universes with positive cosmological constant.
problem Proving topological censorship for spacetimes with positive cosmological constant.
method Developed a new theorem assuming eventual isolation of black hole collections.
result Regions near black hole collections have trivial fundamental group.
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.
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 finds minimum lengths of curves on a one-holed torus.
problem Minimizing the geodesic length of curves on a one-holed torus.
method Explicitly found minima and minimum points of geodesic length functions for a family of curves.
result Concrete examples provided for minimizing geodesic length on hyperbolic surfaces.
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.
It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of …
Paper proves uniqueness of black holes and photon surfaces in higher dimensions.
problem Proving uniqueness of static vacuum black holes and photon surfaces in higher dimensions.
method Combining and generalizing techniques from previous works by Müller zum Hagen, Robinson, and Seifert, the authors prove geometric inequalities for connected (n+1)-dimensional spacetimes.
result Recovering and extending known uniqueness results for black holes and photon surfaces in higher dimensions.
Maximal distortion between geodesic and Euclidean diameters in polygonal domains is studied.
problem Maximal ratio of geodesic to Euclidean diameters in polygonal domains with holes.
method Analyzes convex polygons with holes, using geometric triangulations as a comparison.
result The supremum of the ratio is between and for convex polygons.
Proves uniqueness of black holes in Lovelock gravity, a generalization of Einstein's theory.
problem Proving uniqueness of black holes in Lovelock gravity.
method Combining regularity and rigidity arguments to prove global uniqueness.
result Global uniqueness theorem for extrinsic black holes in Lovelock gravity.
Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying on the interior of Anti-de Sitter (AdS) black holes. We prescribe initial data on a spacelike hypersurface of a Reissner--Nordström--AdS black hole and impose…
We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the Ricci curvature components inside the Reissner-Nordstrom black hole horizons ar…
Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtrationmath.ST
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
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 …
New black hole solutions cannot be rotated without breaking their structure.
problem Proving certain static black hole solutions cannot be deformed into rotating black holes.
method Analyzing specific MKN solutions and proving their static rigidity.
result Proved that some static black hole solutions cannot be deformed into axisymmetric stationary black holes with angular momentum.
We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…
On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holesmath.DG
New static black hole uniqueness theorems for negative cosmological constant.
problem Uniqueness of static black holes in asymptotically locally hyperbolic spaces.
method Inequality relating surface gravity and topology, rigidity of Kottler black holes, monotone quantities under IMCF, regularity theorem for IMCF.
result Static black holes are uniquely determined by their geometry and topology.
We extend a theorem of Masur and Wolf which says that given a hyperbolic surface S, every isometry of the Teichmuller space for S with the Weil-Petersson metric is induced by an element of the mapping class group for S. Our argument handles the previously untreated cases of the four-holed sphere, the one-holed torus, a…
Using ideas from an article of P. Bieliavsky, M. Rooman and Ph. Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by A. Alekseev and Y. Kosmann-Schwarzbach. As an application, I obtain a genuine Poisson structure on which induces a Poisson structure o…
Bartnik mass is positive and non-decreasing for black holes
problem Quasilocal mass for black holes
method Defining a Bartnik mass and proving positivity and monotonicity
result Positive and non-decreasing Bartnik mass for black holes
In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area should be at least . An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemann…
We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime . These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general…
Formula for BPS black hole entropy derived from Vinberg cones.
problem Finding entropy of BPS extremal black holes in non-symmetric scalar manifolds.
method Use of Vinberg's theory of homogeneous cones to determine the inverse of a quadratic map.
result Explicit formula for BPS black hole entropy in any N=2 supergravity with homogeneous scalar manifold.