arXiv subjects

Wontae Kim

Publications and source records attributed to Wontae Kim.

At least 19 recordsLinked to original sources

arXiv2026

Parabolic Poincar\'e inequalities and maximal function estimates for systems of partial differential equations

We study parabolic Poincar\'e inequalities for solutions to nonlinear systems of partial differential equations. Our main results show that these inequalities are self-improving. As applications, we establish reverse H\"older inequalities for the mean oscillation over parabolic cylinders and for the gradient. We also consider the corresponding Poincar\'e inequalities and self-improvement results on time intervals at fixed spatial points. These results are based on a pointwise maximal function estimate. As an application, we obtain regularity results in the time direction for solutions to nonlinear systems.

math.AP↗

arXiv2026

Investigation of the black-hole quantum atmosphere from the effective proper temperature

Hawking radiation may be regarded as originating at the event horizon; however, its spatial origin can instead be distributed over a finite region outside the horizon. In this paper, using an effective proper temperature, we investigate the quantum atmosphere within a tractable model based on the two-dimensional radial sector of $D$-dimensional Schwarzschild black holes. In the Hartle--Hawking state, the proper temperature is derived from the first law of thermodynamics in the presence of the conformal anomaly associated with Hawking radiation. In the Unruh state, we decompose the proper temperature into two chiral temperatures, $T_{\rm L}$ and $T_{\rm R}$, associated with the ingoing and outgoing fluxes, respectively. Demonstrating $T_{\rm R}$ as the effective proper temperature characterizing the outgoing Hawking flux with the proper temperature in the Hartle-Hawking state, we define the atmospheric radius effectively as the radial position at which the effective proper temperature attains its maximum. We then numerically compute the atmospheric radius of the quantum atmosphere for various spacetime dimensions and show that it decreases monotonically as the number of spacetime dimensions increases. In the large-dimensional limit, we find that the atmospheric radius remains separated from the horizon by a finite radial factor, indicating that the quantum atmosphere can persist as an extended exterior region in any dimension.

hep-th↗

arXiv2026

Gauss-Bonnet scalarization of charged qOS-black holes

The Gauss-Bonnet (GB) scalarization for charged quantum Oppenheimer-Snyder (cqOS)-black holes is investigated in the Einstein-Gauss-Bonnet-scalar theory with the nonlinear electrodynamics (NED) term. Here, the scalar coupling function to GB term is given by $f(\phi)=2\lambda \phi^2$ with a coupling constant $\lambda$. Three parameters of mass ($M$), action parameter ($\alpha$), and magnetic charge ($P$) are necessary to describe the cqOS-black hole, and it may become the qOS-black hole when $P=M$. The GB scalarization of cqOS-black holes comes into two cases GB$^\pm$, depending on the sign of GB term which triggers the different phenomena. For $\alpha=0$ and $\lambda>0$, GB$^+$ scalarization is allowed, while for $\alpha\not=0$ and $\lambda<0$, GB$^-$ scalarization appears for a narrow band of $3.5653\le \alpha\le 4.6875$. After discussing the onset GB$^-$ scalarization, we construct scalarized cqOS-black holes which belong to the single branch. The scalar field decays much more rapidly compared to the GB$^+$ case. Stability analysis shows these scalarized black holes are linearly stable under scalar perturbations.

gr-qc↗

arXiv2026

Habilis-$\beta$: A Fast-Motion and Long-Lasting On-Device Vision-Language-Action Model

We introduce Habilis-$\beta$, a fast-motion and long-lasting on-device vision-language-action (VLA) model designed for real-world deployment. Current VLA evaluation remains largely confined to single-trial success rates under curated resets, which fails to capture the fast-motion and long-lasting capabilities essential for practical operation. To address this, we introduce the Productivity-Reliability Plane (PRP), which evaluates performance through Tasks per Hour (TPH) and Mean Time Between Intervention (MTBI) under a continuous-run protocol that demands both high-speed execution and sustained robustness. Habilis-$\beta$ achieves high performance by integrating language-free pre-training on large-scale play data for robust interaction priors with post-training on cyclic task demonstrations that capture state drift across consecutive task iterations. The system further employs ESPADA for phase-adaptive motion shaping to accelerate free-space transit, utilizes rectified-flow distillation to enable high-frequency control on edge devices, and incorporates classifier-free guidance (CFG) as a deployment-time knob to dynamically balance instruction adherence and learned interaction priors. In 1-hour continuous-run evaluations, Habilis-$\beta$ achieves strong performance under the PRP metrics, compared to $\pi_{0.5}$ in both simulation and real-world environments. In simulation, Habilis-$\beta$ achieves 572.6 TPH and 39.2 s MTBI (vs. 120.5 TPH and 30.5 s for $\pi_{0.5}$), while in a real-world humanoid logistics workflow it achieves 124 TPH and 137.4 s MTBI (vs. 19 TPH and 46.1 s for $\pi_{0.5}$). Finally, Habilis-$\beta$ achieves the highest reported performance on the standard RoboTwin 2.0 leaderboard across representative tasks, validating its effectiveness in complex manipulation scenarios.

cs.RO↗

arXiv2026

Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge

It has been proposed that any coupling constant in a covariant action can be treated as a conserved charge by promoting the coupling constant to auxiliary fields, typically realized by a scalar field paired with a higher-form gauge field. However, the procedure may break local symmetries, which can be explicitly shown in a simpler setting such as Maxwell theory. The Hamiltonian analysis of Maxwell theory with the auxiliary fields reveals that some of the constraints are second-class. Applying the BFT formalism, we restore the broken local symmetries and obtain a fully symmetric action defined on an extended configuration space. Despite the restoration of the local symmetries, no additional conserved charges are associated with the recovered symmetries. Consequently, the original theory turns out to be the gauge-fixed version of the extended theory.

hep-th↗

arXiv2025

Very weak solutions to degenerate parabolic double-phase systems

We prove a local self-improving property for the gradient of very weak solutions to degenerate parabolic double-phase systems. The result is based on a reverse H\"older inequality with constants that are independent of the solution. Delicate methods are required to avoid a self-referential argument. In particular, we develop a new phase analysis method.

math.AP↗

arXiv2025

Gradient higher integrability of bounded solutions to parabolic double-phase systems

We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonnegative weight $a$ is $\alpha$-H\"older continuous in space and $\tfrac \alpha 2$-H\"older continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+\alpha$.

math.AP↗

arXiv2025

Gravitational constant as a conserved charge in black hole thermodynamics

Recent work has shown that couplings multiplying individual terms in a Lagrangian can be promoted to conserved charges by introducing scalar-gauge pairs. The gravitational constant, however, plays a qualitatively different role: $G^{-1}$ appears as an overall normalization of the Einstein-Hilbert sector rather than as the coefficient of a single term. In this paper, we show that the gravitational constant can nevertheless be realized as a conserved charge in a modified four-dimensional Einstein-Hilbert theory. Using two scalar-gauge pairs and the quasi-local off-shell Abbott-Deser-Tekin formalism, we construct the conserved charges associated with the mass, the cosmological constant, and the gravitational constant. The resulting charge assignment yields the extended thermodynamic first law and the Smarr formula in a fully consistent manner. Our result therefore extends the conserved-charge interpretation of couplings to the universal gravitational coupling itself in a concrete four-dimensional Einstein-gravity setting.

hep-th↗

arXiv2025

Lightweight and Fast Real-time Image Enhancement via Decomposition of the Spatial-aware Lookup Tables

The image enhancement methods based on 3D lookup tables (3D LUTs) efficiently reduce both model size and runtime by interpolating pre-calculated values at the vertices. However, the 3D LUT methods have a limitation due to their lack of spatial information, as they convert color values on a point-by-point basis. Although spatial-aware 3D LUT methods address this limitation, they introduce additional modules that require a substantial number of parameters, leading to increased runtime as image resolution increases. To address this issue, we propose a method for generating image-adaptive LUTs by focusing on the redundant parts of the tables. Our efficient framework decomposes a 3D LUT into a linear sum of low-dimensional LUTs and employs singular value decomposition (SVD). Furthermore, we enhance the modules for spatial feature fusion to be more cache-efficient. Extensive experimental results demonstrate that our model effectively decreases both the number of parameters and runtime while maintaining spatial awareness and performance.

eess.IV↗

arXiv2025

Strong gravitational lensing effects of black holes with quantum hair

According to the no-hair theorem, stationary black holes are uniquely characterized by their mass, charge, and angular momentum. In this paper, we explore quantum hair by deriving the quantum-corrected black hole metric within the Barvinsky-Vilkovisky formalism. The quantum-corrected metric is obtained perturbatively around flat spacetime without assuming either the commutativity between the nonlocal operator and covariant derivatives or the nonlocal Gauss-Bonnet theorem, both of which are adopted in previous studies. Using this metric, we evaluate the deflection angle in the strong-field limit and compute the associated strong gravitational lensing observables, such as the angular separation and the relative magnification. Our results show that as the quantum hair, determined by the number of virtual massless quantum fields in the nonlocal effective action, increases, the photon sphere radius, the strong deflection angle, and the relative magnification all increase, whereas the angular separation decreases. As a result, we demonstrate that the quantum hair affects not only the black hole geometry but also its strong gravitational lensing effects.

gr-qc↗

arXiv2025

Einstein ring of dust shells with quantum hair

The information about the internal structure of a compact object is classically inaccessible to external observers. In this paper, we investigate how quantum corrections to gravitational fields can reveal the internal structure of compact objects composed of dust shells. Using an effective field theory approach to incorporate quantum corrections up to second order in curvature, we derive a quantum-corrected metric for $N$ uniformly spaced shells with equal surface mass density and then examine how these corrections manifest in the deflection angle for gravitational lensing. In particular, we mainly investigate quantum-corrected astrophysical observables such as the Einstein ring and image magnification. Compared to the classical scenario, the deflection angle and the corresponding Einstein angle differ by a term that depends explicitly on the number of dust shells, which play the role of quantum hair. Specifically, the quantum correction to them diminishes as $N$ increases, yet a finite deviation from the classical result remains even in the continuum limit $N\to\infty$. Consequently, our results show that the internal structures of compact objects with identical mass and radius can be distinguished by quantum hair through their lensing observables.

gr-qc↗

arXiv2025

Existence, uniqueness and regularity for elliptic $p$-Laplace systems with complex coefficients

This paper concerns elliptic systems of $p$-Laplace type with complex valued coefficient and source term. We extend the real valued theory of the elliptic $p$-Laplace equation to the complex valued case. We establish the existence and uniqueness of solutions to the Dirichlet problem and prove the Schauder estimate in the case of H\"older continuous coefficients and source terms. We also consider families of coefficient functions parametrized by a complex variable and prove a differentiability result for the map taking the complex parameter to the corresponding solution.

math.AP↗

arXiv2024

Calder\'on-Zygmund type estimate for the singular parabolic double-phase system

This paper discusses the local Calder\'on-Zygmund type estimate for the singular parabolic double-phase system. The proof covers the counterpart $p<2$ of the result in [23]. Phase analysis is employed to determine an appropriate intrinsic geometry for each phase. Comparison estimates and scaling invariant properties for each intrinsic geometry are the main techniques to obtain the main estimate.

math.AP↗

arXiv2024

Validity of black hole complementarity in an accelerating Schwarzschild black hole

Black hole complementarity has been well understood in spherically symmetric black holes. To study its validity for an accelerating Schwarzschild black hole, which has a preferred direction, we perform the thought experiment proposed by Susskind and Thorlacius and further investigate the criteria set by Hayden and Preskill. First, we derive thermodynamic quantities that satisfy the first law of thermodynamics. Using these quantities, we conduct thought experiments based on the Page time and the scrambling time, which show that black hole complementarity remains valid, although the energy required for the duplication of information depends on the angle due to the axisymmetric metric.

gr-qc↗

arXiv2024

The quasilocal energy and thermodynamic first law in accelerating AdS black holes

We scrutinize the conserved energy of an accelerating AdS black hole by employing the off-shell quasilocal formalism, which amalgamates the ADT formalism with the covariant phase space approach. In the presence of conical singularities in the accelerating black hole, the energy expression is articulated through the surface term derived from our formalism. The essence of our analysis of the quasilocal energy resides in the surface contributions coming from the conical singularities as well as the conventional radial boundary. Consequently, the resultant conserved quasilocal energy naturally conforms the thermodynamic first law for the black hole without necessitating any augmentation of thermodynamic variables.

hep-th↗

arXiv2024

H\"older regularity for degenerate parabolic double-phase equations

We prove that bounded weak solutions to degenerate parabolic double-phase equations of $p$-Laplace type are locally H\"older continuous. The proof is based on phase analysis and methods for the $p$-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the $p$-Laplace or the $q$-Laplace equation.

math.AP↗

arXiv2023

Quantum geodesics reflecting the internal structure of stars composed of shells

In general relativity, an external observer cannot distinguish distinct internal structures between two spherically symmetric stars that have the same total mass $M$. However, when quantum corrections are taken into account, the external metrics of the stars will receive quantum corrections depending on their internal structures. In this paper, we obtain the quantum-corrected metrics at linear order in curvature for two spherically symmetric shells characterized by different internal structures: one with an empty interior and the other with $N$ internal shells. The dependence on the internal structures in the corrected metrics tells us that geodesics on these backgrounds would be deformed according to the internal structures. We conduct numerical computations to find out the angle of geodesic precession and show that the presence of internal structures amplifies the precession angle reflecting the discrepancy between the radial and orbital periods within the geodesic orbit. The amount of the precession angle increases monotonically as the number of internal shells increases and it eventually converges to a certain value for $N \to \infty$.

gr-qc↗

arXiv2023

Investigation of black hole complementarity in AdS$_2$ black holes

Black hole complementarity plays a pivotal role in resolving the information loss paradox by treating Hawking radiation as carriers of information, apart from the complicated mechanisms involved in decoding information from this radiation. The thought experiment proposed by Susskind and Thorlacius, as well as the criteria set forth by Hayden and Preskill, provide deep insights into the intricate relationship of black hole complementarity between fiducial and infalling observers. We execute the Alice-Bob thought experiment in the context of two-dimensional anti-de Sitter black holes. It turns out that information cloning can be avoided in the case of a large black hole. According to the Hayden-Preskill criteria, the scale parameter associated with the explicit breaking of the one-dimensional group of reparametrizations must significantly exceed the squared mass of the black hole to effectively prevent information cloning.

hep-th↗