Proves rigidity of extremal Kerr-Newman horizons.
problem Classifying near-horizon geometries of extremal Kerr-Newman horizons.
method Proves intrinsic geometry constraints leading to rigidity.
result Proves extremal Kerr-Newman horizons are unique.
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48 results for “extremal horizons”
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.
Proves uniqueness of certain spacetime solutions with extremal horizons.
problem Proving uniqueness of extremal Schwarzschild de Sitter spacetime solutions.
method Analytic proof in four and higher dimensions, spectral problem for hyperbolic surfaces.
result Proves extremal Schwarzschild de Sitter solutions are unique up to identifications.
Proves symmetries of extremal horizons in spacetimes.
problem Proving symmetries of extremal horizons in arbitrary dimensions.
method Analyzes Killing vector fields and near-horizon geometry.
result Enhanced isometry groups and shifted Aretakis instability.
Proves intrinsic rigidity of extremal horizons, classifying their geometry.
problem Classifying the intrinsic geometry of extremal horizons.
method Proves existence of Killing vector fields and solves PDEs.
result Proves most general solution for extremal Kerr horizon and classifies near-horizon geometries.
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 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 consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of a…
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.
We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold …
We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface …
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 leading to stable solutions.
Study on instability of extreme Reissner-Nordström spacetime perturbations.
problem Linear stability of gravitational and electromagnetic perturbations in extreme Reissner-Nordström spacetime.
method Extends Giorgi's framework to prove instability results for a set of gauge invariant quantities along the event horizon.
result Proves decay, non-decay, and polynomial blow-up estimates for certain quantities along the event horizon, depending on the number of derivatives.
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.
This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial da…
Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.
problem Analyzing decay and non-decay rates of solutions to the massless Vlasov equation on Reissner-Nordström spacetimes.
method Quantitative analysis of geodesic flow and comparison to wave equation instability results.
result Exponential decay rates in subextremal cases and polynomial rates in extremal cases, with non-decay of transversal derivatives in extremal cases.
We provide bounds on the first Betti number and structure results for the fundamental group of horizon cross-sections for extreme stationary vacuum black holes in arbitrary dimension, without additional symmetry hypotheses. This is achieved by exploiting a correspondence between the associated near-horizon geometries a…
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 study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with spacelike or null infinity, and we solve the linear wave equation on the domain …
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 …
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…
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.
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjust…
New rigidity results for quasi-Einstein metrics with non-zero divergence-free vector fields.
problem Classifying quasi-Einstein metrics with specific vector field properties.
method Analyzing quasi-Einstein metrics on closed manifolds and near-horizon geometries of extreme black holes.
result These metrics always admit a one-parameter group of isometries generated by the divergence-free vector field.
We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the future event horizon. We show that such an estimate requires 1) a higher degree of…
New insights into black hole horizons from asymptotic expansions.
problem Understanding the geometry of black hole horizons.
method Proving the asymptotic expansion of spacetime metrics at non-degenerate Killing horizons.
result The full asymptotic expansion of smooth vacuum metrics at non-degenerate Killing horizons is determined by the horizon geometry.
This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a quantile spectral beta representation of risk based on the decomposition of cova…
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 consider solutions to the linear wave equation on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In particular, no symmetry is assumed on initial data, and the support of the solutions may con…
DMIDAS improves long-term forecasting accuracy in healthcare and electricity data.
problem Challenging long-term forecasting accuracy and computational complexity.
method Smoothness regularization and mixed data sampling techniques integrated into NBEATS architecture.
result Improves prediction accuracy by 5% on long forecasting horizons (1000 timestamps) compared to state-of-the-art models.
We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased estimators, but is known to suffer from an excessively high variance in long-horizon pr…
The Area-Angular Momentum-Charge Inequality for Black Holes With Positive Cosmological Constantgr-qc
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previous inequalities of this type, the proof is reduced to minimizing an `ar…
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 a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-t…
We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies and . In addition to t…
The study shows black hole horizons at low temperatures have limited topology.
problem Topology of black hole horizons at low temperatures.
method Almost nonnegative generalized -Bakry-Émery Ricci curvature, diameter upper bound, volume lower bound.
result Low temperature black hole horizons have limited topology.
Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific task of choosing among distributions to use for random hyperparameter optimization.…
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.
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.
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.
We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathematical theorem which is a straightforward consequence of a type of energy conditi…
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positi…
HODL Strategy or Fantasy? 480 Million Crypto Market Simulations and the Macro-Sentiment Effectq-fin.ST
Crypto simulations show HODL strategy loads risk onto most investors, with macro-sentiment affecting returns.
problem Understanding real risk-return trade-offs and factors affecting crypto returns.
method Two independent analyses: 480 million Monte Carlo simulations and Bayesian multi-horizon local projection framework.
result HODL strategy exposes most investors to extreme downside risk, and macro-sentiment conditions are dominant indicators for future outcomes.
This paper presents a novel scaling method for unbiased risk estimation.
problem Challenges in risk assessment due to limited data, non-stationarity, and heavy tails.
method Develops a statistical framework for efficient risk scaling, extending beyond the square-root-of-time rule.
result Ensures robust and conservative risk estimation, applicable to small sample settings.
We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Li…
Probabilistic NDVI forecasting from sparse satellite data.
problem Challenges in short-term NDVI forecasting due to sparse and irregular satellite data.
method Probabilistic forecasting framework using historical NDVI and meteorological observations, with temporal-distance weighted quantile loss and extreme-weather feature engineering.
result The proposed method outperforms baselines on pointwise and probabilistic evaluation metrics.
We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a viable solution strategy that scales extremely well with the number of CPUs avail…
Computational models that forecast the progression of Alzheimer's disease at the patient level are extremely useful tools for identifying high risk cohorts for early intervention and treatment planning. The state-of-the-art work in this area proposes models that forecast by using latent representations extracted from t…