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.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Horizons”
Develops a formalism for studying general horizons and derives a near-horizon equation.
problem Analyzes the geometry of general horizons in spacetime.
method Introduces a formalism based on encoding the zeroth and first transverse derivatives of the deformation tensor on null hypersurfaces.
result Derives a generalized near-horizon equation that holds on any horizon.
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…
Proves uniqueness of near-horizon geometries from degenerate Kerr black holes.
problem Proving uniqueness of near-horizon geometries from degenerate Kerr black holes.
method Proof of uniqueness within the collection of nearby vacuum near-horizon geometries.
result Uniqueness of near-horizon geometries from degenerate Kerr black holes proven.
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.
The study reveals distinct patterns in retail investors' holding periods affecting stock returns.
problem Understanding the impact of retail investors' investment horizons on stock returns.
method Using self-reported holding periods from StockTwits, the study categorizes retail investors into long-horizon and short-horizon groups and analyzes their return patterns.
result Long-horizon retail investors exhibit underreaction to earnings announcements, while short-horizon investors show overreaction.
Paper studies apparent horizon dynamics and introduces a null comparison principle.
problem Global dynamics of apparent horizon and local achronality.
method Constructing apparent horizon by solving MOTS along null hypersurfaces, using Klainerman-Szeftel estimates and null comparison principle.
result Smooth, asymptotically null, and converging apparent horizon proven.
The article discusses new horizons in black hole physics.
problem Conceptual limitations of event horizons in black hole studies.
method Use of quasi-local horizons to generalize mechanics of black holes.
result Laws governing quasi-local horizons generalize those for event horizons.
Solves consumption-investment problem with random horizon under Epstein-Zin preferences.
problem Maximizing consumption and investment under random time horizons with Epstein-Zin utility.
method Backward stochastic differential equations with superlinear growth on unbounded random horizons.
result Optimal strategies differ significantly when moving from fixed to random time horizons.
Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.
problem Examining the behavior of Wang-Yau quasi-local energy near apparent horizons in strong fields.
method Analyzing the limit of the Wang-Yau quasi-local energy as a spacelike surface approaches an apparent horizon, considering bounded coordinate functions and spacelike mean curvature.
result The limit of the Wang-Yau quasi-local energy falls into two cases: it blows up or remains finite, depending on whether the horizon can be isometrically embedded into .
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.
This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon . Secondly, we exemplify that the expected utility stemming from applying th…
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.
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.
Confidence Horizonsstat.ME
The paper proposes confidence horizons for anytime-valid inference with finite time constraints.
problem The need for stopping experiments early with valid inference under finite time horizons.
method Confidence horizons as large-sample confidence sequences or group sequential repeated confidence intervals.
result It is possible to obtain sharper large-sample anytime-valid inference by forgoing validity beyond a finite time horizon.
Study proves no degenerate horizons in static vacua.
problem Existence of degenerate horizons in static vacua.
method Differential geometry and Bakry-Émery-Ricci bounds.
result Degenerate horizons do not exist in static vacuum configurations.
ElasTST improves time-series forecasting across varying horizons.
problem Robust forecasting across different time horizons in varied industrial sectors.
method Elastic Time-Series Transformer (ElasTST) with non-autoregressive design, rotary position embedding, and multi-scale patching.
result ElasTST provides robust forecasts across varying horizons without retraining.
Proves conditions for Cauchy horizons in low-regularity spacetimes.
problem Conditions for the existence of Cauchy horizons in spacetimes with low regularity.
method Analyzes the relationship between complete Cauchy hypersurfaces, almost closed causal curves, and points at infinity.
result Wald's conjecture reformulated as a PDE problem about Cauchy horizons.
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.
Is Long Horizon Reinforcement Learning More Difficult Than Short Horizon Reinforcement Learning?cs.LG
Long horizon reinforcement learning is as hard as short horizon learning.
problem Understanding the difficulty of long horizon reinforcement learning problems.
method Introduced new concepts: ε-net for optimal policies and Online Trajectory Synthesis algorithm.
result Proved that sample complexity scales logarithmically with the planning horizon, refuting the conjecture.
Regularized greedy policies outperform classical greedy in finite-horizon bandit problems.
problem Optimizing decision-making in sequential experiments with finite time constraints.
method Developed regularized greedy algorithms for multi-armed Bernoulli bandits.
result Calibrated regularized greedy policies consistently match or outperform state-of-the-art algorithms.
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 first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…
Paper proves existence of anisotropic dynamical horizons in gravitational collapse.
problem Existence of apparent horizons in gravitational collapse.
method Scale-critical hyperbolic method and non-perturbative elliptic techniques.
result Smooth and spacelike apparent horizons emerge from general initial data in gravitational collapse.
Short-horizon bias causes meta-optimization to favor small learning rates.
problem Short-horizon bias in meta-optimization leads to suboptimal learning rates.
method Analyzes a noisy quadratic cost function and runs meta-optimization experiments on benchmark datasets.
result Meta-optimization chooses too small a learning rate, even with a long time horizon.
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…
New risk measure considers horizon risk and interest rate uncertainty.
problem Dynamic risk evaluation considering horizon risk and interest rate uncertainty.
method Introduced a risk measure based on generalized Tsallis entropy.
result New q-entropic risk measure quantifies capital requirement.
Extends Killing vector fields to beyond compact Cauchy horizons.
problem Proves existence of Killing vector fields beyond compact Cauchy horizons.
method New unique continuation theorem for wave equations through smooth compact lightlike hypersurfaces; novel Carleman type estimate.
result Killing vector field exists on both sides of the horizon.
The paper examines differentiability of horizons along their generators in Lorentz manifolds.
problem Analyzing the differentiability of horizons along their generators in Lorentz manifolds.
method Using a result that every mathematical horizon locally coincides with a Cauchy horizon, the paper proves conditions for differentiability of horizons.
result Horizons are either continuously differentiable or have differentiability jumping points.
Optimizes investment under uncertain time horizons with non-concave utility.
problem Optimizing investment decisions with non-concave utility and uncertain time horizons.
method Established necessary and sufficient conditions for optimality, suggested recursive procedure for non-concave utility.
result Optimal investment strategies under uncertain time horizons exhibit multimodal distribution, indicating flexibility in switching between local maximizers.
WSqD extends learning rate schedules for large model training without fixed horizons.
problem Fixed learning rate schedules limit training horizon extension.
method WSqD replaces constant stable phase with a shifted inverse-square-root base, retaining linear cooldown.
result WSqD achieves minimax-optimal convergence rate and horizon-independence.
The article calculates the near horizon limit of Wang--Yau quasi-local mass.
problem Calculating the near horizon limit of quasi-local mass.
method Utilizing the properties of the mean curvature vector and optimal embedding equation.
result Existence and uniqueness of optimal embedding and continuity of quasi-local mass.
Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifo…
This paper improves LSTM networks for long-term forecasts.
problem Challenges in long-horizon forecasting using LSTM networks.
method Expectation-biased LSTM architectures and methods.
result Significantly improved long-horizon forecasting performance.
The study proves the existence and uniqueness of near-horizon geometries for 5D black holes.
problem Existence and uniqueness of near-horizon geometries for 5-dimensional black holes.
method Proved existence and uniqueness of bi-axisymmetric near-horizon geometries with specific topologies and charges.
result Existence and uniqueness of near-horizon geometries for 5D black holes established up to isometry.
The study classifies compact Cauchy horizons in vacuum spacetimes.
problem Classifying compact Cauchy horizons in vacuum spacetimes.
method Complete classification theorem based on topology and null generators.
result Different cases of compact Cauchy horizons with specific manifolds and spacetime properties.
This paper challenges the conventional wisdom of trend-following by showing that the medium-term horizon adds little value once short- and long-term components are included.
problem The conventional wisdom that more horizons improve diversification and performance is challenged.
method A Bayesian optimization framework reallocates exposure dynamically across horizons, optimizing horizon-level weights at the asset level and applying sparsity and turnover control for dynamic allocation across assets.
result The medium-term horizon contributes little incremental performance or diversification once short- and long-term components are included.
We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein's equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black holes. The simplest examples give horizons of spatial topology S^3xS^2 or the non-tr…
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
problem Confirming the Kruskal-Szekeres extension for Schwarzschild spacetime.
method Reformulating the problem as an ODE and showing the ODE admits a solution if and only if the horizon is non-degenerate.
result Photon surfaces approaching the Killing horizon must necessarily cross it.
Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant non-zero surface gravitymath.DG
Proves symmetry in vacuum spacetimes with compact Cauchy horizons.
problem Symmetries in vacuum spacetimes with compact Cauchy horizons.
method Solving Killing equation up to infinite order at the Cauchy horizon, extending the solution to the globally hyperbolic region.
result Maximally globally hyperbolic vacuum development cannot be extended across compact Cauchy horizons.
The study applies Riemannian flow theory to Lorentzian manifolds to understand horizons.
problem Understanding the geometry of horizons in Lorentzian manifolds.
method Importing results from Riemannian flows to Lorentzian horizons, clarifying the relation between isometric/geodesible flows and non-degeneracy conditions.
result Theorems on the dynamical structure of compact horizons without relying on degeneracy assumptions.
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…
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.
Study wave equations on compact Cauchy horizons with unique solutions.
problem Existence and uniqueness of solutions to wave equations near compact Cauchy horizons.
method Energy estimates and Cauchy horizon analysis for wave equations on vector bundles.
result Unique solution to wave equations on globally hyperbolic region if initial data is given on Cauchy horizon.
Reward tweaking optimizes behavior for long-term goals by adjusting the reward function.
problem Optimizing behavior for long-term goals in reinforcement learning with unstable long planning horizons.
method Reward tweaking learns a surrogate reward function that induces optimal behavior for the original task.
result Reward tweaking guides agents towards better long-term returns while planning for short horizons.
Unified RNN architecture improves multi-time-horizon solar forecasting.
problem Large prediction errors in traditional solar forecasting methods.
method Recurrent Neural Network (RNN) for multi-time-horizon solar forecasting.
result Lower root-mean-squared prediction error compared to previous methods.
Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.
problem Analyzing transverse expansion of metric on null hypersurfaces.
method Covariant approach, general geometric identities, generalized symmetry generators.
result Transverse expansion of spacetime metric uniquely determined at non-degenerate Killing horizons.
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…