We study real source-free Maxwell fields on slowly rotating, weakly charged Kerr-Newman exteriors and set up a finite-energy scattering theory after removal of the stationary Coulomb sector. The conserved electric and magnetic fluxes account exactly for the two-dimensional stationary non-decaying part, giving a natural decomposition of the Maxwell Cauchy space into stationary and charge-free radiative parts. For the radiative field, the paper develops a finite-order transfer mechanism from regular spin-one curvature variables back to the Maxwell tensor field, combining red-shift control, far-field hierarchy, trapped-set analysis, a Fredholm argument ruling out real-frequency modes, and same-order reconstruction of the middle components. Under the stated slow-weak master estimates, this gives uniform boundedness, integrated local energy decay, radiation fields, wave operators, and asymptotic completeness for the stationary-subtracted Maxwell evolution, with the Kerr case recovered as a special subcase and the charged rotating case reduced to explicit geometric and analytic estimates.

In this paper, we show the uniform energy decay estimates for the Maxwell-Higgs system in the outer region of Schwarzschild spacetimes using the integrated local energy decay (ILED) estimate and the geometric energy estimates to bound on the middle component of the Maxwell-Higgs system. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

We study small-data solutions of a nonlinear scalar field equation on spatially flat d-dimensional FLRW spacetimes (d >= 4). In conformal time tau the field satisfies a damped semilinear wave/Klein-Gordon equation with time-dependent coefficients determined by the scale factor a(tau) and the conformal Hubble rate H(tau) = (a) over dot/a. We focus on accelerated conformal expansion of the form H(tau) = H-0(1 + tau)(-alpha) with H-0 > 0 and 0 < alpha < 1, for which a(tau) grows stretched-exponentially, and we assume a power potential V(phi) = -epsilon/m+1|phi|(m+1). For global solutions arising from sufficiently small, spatially localized initial data, we introduce the conformal rescaling phi = a((d-2)/2)phi, which removes the first-order Hubble damping and exposes the interaction as a time-dependent coupling. In the rescaled equation the nonlinearity is weighted by g(tau) = a(tau)sigma with sigma = d + 2-(d-2)m/2, so the conformal power m(conf) = d+2/d-2 is the sharp threshold for redshift suppression: g decays for m > m(conf), is constant for m = m(conf) (classical conformal invariance), and grows for 1 < m < m(conf). For accelerated conformal expansion H(tau) = H-0(1 +tau)(-alpha) with 0 < alpha < 1 and for superconformal interactions m > m(conf), we prove that g is an element of L-1([0, infinity)) and deduce small-data global existence together with scattering/asymptotic linearization for phi. As a complementary result in the diffusion-dominated regime 1 < m < 1 + 2/d-1, we adapt a weighted energy method for variable damping to deduce explicit L-2 and L-1 decay rates of the form parallel to phi(tau, center dot)parallel to(L2) less than or similar to a(tau)(-2/(m-1))(1 + tau)(-(1+alpha)(1/m-1-d-1/4)) parallel to phi(tau, center dot)parallel to(1)(L) less than or similar to a(tau)(-2/(m-1))(1 +tau)(-(1+alpha)(1/m-1-d-1/2).) These bounds provide a quantitative PDE formulation of redshift-induced suppression of nonlinear scalar self-interactions at late conformal times. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

We propose a mechanism to control magnetic skyrmion motion by generating a skyrmion number current. This current is produced and controlled via an explicitly time-dependent Hamiltonian containing a Zeeman term arising from the interaction between the spin system and circularly polarized light. We find that skyrmion dynamics exhibit a limit cycle in momentum space, whose properties are determined only by physical parameters: the magnitude of the external magnetic field, the Heisenberg coupling, and the Gilbert damping constant. This method provides a theoretical explanation for the topological origin of optically controlled skyrmion motion, and it opens the possibility for efficient, low-dissipation skyrmion control using skyrmion number currents as an alternative to electric currents.

In this paper, we study a cosmological model that combines Nonlinear Electrodynamics (NLED) with a cosmological constant in an anisotropic Bianchi type I spacetime. The dynamic equations are derived from Einstein's field equations and the conservation of the energy-momentum tensor. A perturbative scheme with a small anisotropy parameter e << 1 is employed, leading to a non-singular scale factor with a finite minimum b(min) = root gamma. For sufficiently small values of the parameter delta = beta Lambda K-2, the early accelerated expansion is dominated by the NLED field; otherwise, the cosmological constant (A) also contributes significantly. At late times, A completely dominates and drives the accelerated expansion of the universe. Phase-space analysis is performed to identify the critical points and describe the transitions in cosmic evolution. The results show that the model yields a non-singular universe, exhibits isotropization, and can naturally connect early inflation with late-time acceleration through an intermediate decelerating phase. These findings highlight the potential of NLED with a cosmological constant as a viable framework for explaining both accelerated epochs in anisotropic cosmology.

The Skyrmion number density, q equivalent to n ->partial derivative xn -> x partial derivative yn ->/4 pi , is one of the key quantities that characterizes the topological properties of Skyrmionic spin textures. In this work, we propose a topologically supported stabilization mechanism for two-dimensional magnetic Skyrmions using a Hamiltonian that includes a term proportional to the square of the Skyrmion number density, q2. This term, derived from the generalization of the harmonic map, preserves inversion symmetry and remains significant under strong external magnetic fields where conventional exchange interactions are suppressed. Through scaling analysis and micromagnetic calculations using the Landau-Lifshitz-Gilbert equation, we show that this q2 term stabilizes single Skyrmion configurations. We also derive an energy bound that confirms the topological protection of these configurations under radial perturbation. Our results provide a framework for realizing Skyrmions in materials without broken inversion symmetry, particularly in systems subjected to strong external magnetic fields, where conventional exchange interactions are significantly weaker than the Zeeman effect.

We address the strong CP problem: why the physical QCD angle theta-bar must be extraordinarily small given the stringent bounds on the neutron electric dipole moment. Peccei-Quinn axion models can relax theta-bar dynamically, but rely on an approximate global symmetry expected to be violated by quantum gravity and face severe astrophysical and cosmological constraints. We propose Discrete theta Projection, an axionless, gauge-protected resolution obtained by gauging a finite cyclic subgroup Z_Nof the 2π shift symmetry of theta. Coupling QCD to a compact, local and gapped topological sector orbifolds the path integral, identifying theta values that differ by 2π/N and admitting only instanton sectors whose topological charge lies in Z_N. In the large four-volume limit the vacuum energy becomes the lower envelope of the orbifold images, so the theory dynamically selects the branch closest to the CP-symmetric point, enforcing || ≤ π/N without assuming any prior smallness. Because the discrete shift is gauged, continuous renormalization of theta is forbidden; the construction can be formulated via higher-form/two-group structure with integer-quantized couplings fixed by anomaly inflow, ensuring radiative and gravitational stability and satisfying mixed gauge-gravity consistency conditions. The framework predicts a neutron EDM suppressed by 1/N, no axion signatures, no domain-wall/isocurvature issues, and lattice diagnostics: piecewise-analytic theta dependence with cusps at odd fractions of the reduced period and a global curvature scaling as 1/N^2. We provide the EFT construction, a nonperturbative proof of vacuum projection, a full anomaly analysis, and UV embeddings (including discrete clockwork chains) that generate large effective N while preserving integrality and consistency throughout.

We study the neutral massive Maxwell (Proca) equation on subextremal Reissner–Nordström exteriors. After spherical-harmonic decomposition, the odd sector is scalar, while the even sector remains a genuinely coupled 2×2 system. Our starting point is that this even system admits an exact asymptotic polarization splitting at spatial infinity. The three resulting channels carry effective angular momenta ℓ-1, ℓ, and ℓ+1, and these are precisely the indices that govern the late-time thresholds. For each fixed angular momentum we develop a threshold spectral theory for the cut-off resolvent. We prove meromorphic continuation across the massive branch cut, rule out upper-half-plane modes and threshold resonances, and obtain explicit small- and large-Coulomb expansions for the branch-cut jump. Inverting this jump yields polarization-resolved intermediate tails together with the universal very-late t^-5/6 branch-cut law. At the full-field level, high-order angular regularity allows us to sum the modewise leading terms on compact radial sets and obtain a two-regime asymptotic expansion for the radiative branch-cut component of the Proca field, with explicit coefficient fields and quantitative remainders. We also analyze the quasibound resonance branches created by stable timelike trapping, prove residue and reconstruction bounds, and derive a fully self-contained dyadic packet estimate. As a result, the unsplit full Proca field obeys logarithmic compact-region decay, while the radiative branch-cut contribution retains explicit polynomial asymptotics and explicit leading coefficients.

We present a non-singular, definition-level formulation of F-theory by replacing the traditional shrinking-fiber limit of M-theory with compactification on a tower-completed circle described using perfectoid geometry and condensed mathematics. This construction provides an intrinsic eleven-dimensional carrier for modular data and admits a canonical tilting and comparison procedure that yields elliptic geometry as an output rather than an auxiliary input. Using this framework, we establish a precise M-theory/Type IIB dictionary in the constant-coupling sector, showing how the physical axio-dilaton is fixed by eleven-dimensional geometric and topological data. The correspondence is tested at the level of the ten-dimensional bosonic effective action, including its topological couplings inherited from eleven dimensions. The tower-completed geometry naturally organizes global sectors in generalized cohomology, with charge data governed by K-theory and exhibiting a canonical prime-power torsion structure. We further show how this framework extends to varying-coupling backgrounds and duality defects, admits a natural adelic completion with prime-independence, and generalizes to higher-rank and U-duality geometries. We also discuss holographic aspects and the anomaly-refined extension of the duality group beyond the bosonic truncation. Together, these results provide a coherent, non-singular foundation for F-theory and its extensions.

We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved energy is proved positive, the complete affine threshold obstruction is identified, and all remaining finite-energy dynamics are shown to be uniformly stable with no unstable modes. This is the sharp statement for compact reflecting slabs, where genuine time decay is false in general. We then extend the same threshold philosophy to black-hole exteriors, separating the intrinsic conformal mechanism from the exterior scalar-wave inputs needed for red-shift, local energy, limiting absorption, and zero-frequency control. The framework gives main applications to Kerr, Reissner-Nordström, slowly rotating weakly charged Kerr-Newman wall exteriors, and extremal horizon-charge obstructions. Our precise result is that it proves stability only for the conformal scalar-curvature sector, not tensorial or nonlinear gravitational stability, and it distinguishes boundedness, qualitative local decay, polynomial decay, and extremal Aretakis-type obstruction without conflating them.

We develop a small-data Maxwell–Higgs theory on Schwarzschild and slowly rotating Kerr black-hole exteriors for gauge-invariant nonnegative self-interactions near the trivial vacuum. The Schwarzschild part gives a complete global, radiative, and scattering theory, while the slowly rotating Kerr part gives a robust massless forward theory and a perturbative small-electric extension. The main mechanism is a transfer principle: once the required linear energy, decay, horizon, and far-field estimates are available, the nonlinear Lorenz-gauge problem yields global existence, gauge-covariant radiation fields, nonlinear wave operators, and asymptotic completeness. The Coulomb-sector analysis identifies the correct long-range normalization in fixed electric sectors and separates the genuinely proved results from the remaining rotating massive final-state problems. All Kerr scattering statements beyond the established massless and small-electric forward regimes are stated explicitly under their necessary spectral and final-state conditions, namely, no rapid-rotation, large-charge, and unconditional massive rotating scattering.

We study lepton-flavor-violating (LFV) decays of a heavy Higgs boson, H → μτ, in the Type-III two-Higgs-doublet model by recasting the CMS search at √(s) = 13 TeV with 35.9 fb^-1 using fast detector simulation in the mass range 200-450 GeV. We develop a deep neural network (DNN) classifier trained on final-state kinematic variables that, with mass-dependent threshold optimization, reduces the expected 95

In this paper, we report the results of comparing the effect of using trace of stress-energy tensor versus real-valued scalar field in Nonminimal Derivative Coupling gravitation model, respectively, denoted as NMDC-T and NMDC-phi. We employ the model into an incompressible star and see the effect of both models NMDC-T and NMDC-phi on the compactness and mass-radius relation. We find that coupling parameters of NMDC-T are less sensitive than NMDC-phi.

We propose a mechanism to control the motion of magnetic Skyrmions through the generation of a Skyrmion number current. This current is induced and tuned by an explicitly time-dependent Hamiltonian that includes a Zeeman term arising from the interaction between the spin system and circularly polarized light. To capture the effect, we apply a first-order perturbation method to the Landau-Lifshitz-Gilbert equation, using a breathing Skyrmion ansatz based on the Belavin-Polyakov profile. This approach reveals that the time-dependent deformation of the Skyrmion boundary produces an anisotropic breathing mode, which in turn generates a nonzero Skyrmion number current. The resulting dynamics in momentum space form a limit cycle, whose characteristics depend solely on the external magnetic field amplitude, the Heisenberg exchange coupling, and the Gilbert damping constant. Our formulation not only clarifies the topological origin of optically driven Skyrmion motion but also points to Skyrmion number currents as a low-dissipation alternative to electric currents for efficient Skyrmion control.

In this paper, we elucidate the problem of gravitating skyrmion governed by the field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry is assumed and both the metric functions and Skyrme ansatz depend on the radial and retarded time coordinates implying that the system is dynamic. We show that unique global smooth solutions of the Einstein-Skyrme system with topological charge B = 1, that are assumed to be monotonically decreasing with respect to the radial coordinate and infinitely differentiable at the neighborhood of the origin, exist if we constrain the initial data and the coupling constant must fall in certain finite intervals that are deduced from the sufficient conditions of fixed-point theorem. We also discuss the possible configurations within the Einstein-Skyrme system which develop singularities in coordinate origin.

We study cosmological perturbations in the minimal theory of mass-varying massive gravity (MTMVMG), a constrained extension of mass-varying massive gravity that propagates only three physical degrees of freedom. We show that MTMVMG admits a stable cosmological solutions i.e. free from ghost, gradient, and tachyonic instabilities around the homogeneous and isotropic background. We further demonstrate that the dynamical external scalar field––which is responsible for the mass of the graviton––can suitably serve as either dark energy or the inflaton, yielding a description consistent with current cosmological observations.

We consider a spherically symmetric homogeneous perfect fluid undergoing a gravitational collapse to singularity in the framework of higher-dimensional Rastall gravity in the cases of vanishing and nonvanishing cosmological constants. The possible final states of the collapse in any finite dimension are black hole and naked singularity, but the naked singularity formation becomes less favored when the dimension is increased. We find that there are two physically distinct solutions for the collapse evolution in the case of nonzero cosmological constant: trigonometric and exponential solutions. The effective energy density of the fluid is decreasing (increasing) in the former (latter) when the magnitude of the cosmological constant is increased, which implies that the former undergoes a slower collapse than the latter. Furthermore, we find that a temporary trapped surface is possible to emerge in the case of trigonometric solution in the naked singularity region only. Therefore, distant observers with observational time shorter than the collapse duration may conclude that a black hole is formed, although the collapse will eventually lead to a naked singularity formation.

In this paper, we obtain L infinity estimate for the Maxwell-Higgs system in the exterior region of Reissner-Nordstr & ouml;m spacetimes. Utilizing the integrated local energy decay estimate, the Sobolev embedding theorem alongside the Gagliardo-Nirenberg-Sobolev inequality on compact Riemannian manifold, we derive the boundedness for L infinity norm of the Maxwell-Higgs system on Reissner-Nordstr & ouml;m geometry.

In this paper, we study the local existence of a classical solution to the coupled Einstein and Maxwell-Klein-Gordon system in higher dimensions. This system provides a toy model to study the dynamics of the complex scalar fields under the influence of the interaction of the gravitational and electromagnetic fields. In the starting point, we introduce the metric of the space-time in the Bondi coordinate. Then, we construct the evolution equation in the form of a single first-order nonlinear integro-differential equation. Furthermore, we show that there exists a unique fixed point that is the solution of the main problem based on the contraction mapping arguments. Finally, for a given initial data, we prove the existence of a local classical solution.