In this paper, wave solutions to the classical Yang-Mills equations with <italic>SU</italic>(2) symmetry are investigated in the region outside field sources. They represent a significant generalization of the solutions found in our previous publication describing non-Abelian transverse progressive waves propagating in the direction of the Cartesian <italic>z</italic>-axis. In the new paper, wave solutions to the considered system of nonlinear partial differential equations are sought in a special form. In it, the unknown functions are presented as some complex series and for their coefficients, depending on the wave phase, a system of recurrence relations is obtained. This paper proves that in the examined region, the considered complex series are absolutely convergent. They allow us to determine a wide class of non-Abelian wave solutions to the Yang-Mills equations. In addition, exact wave solutions in closed form are found, which describe the asymptotic behavior of the considered non-Abelian wave solutions for large distances from the <italic>z</italic>-axis.

Russia

Alexander S. Rabinowitch

On a wide class of solutions of SU(2) Yang–Mills equations describing non-Abelian progressive waves

By means of the deformed trigonometric Calogero-Sutherland (CS) operator, we construct a family of commuting operators via nested commutators. In terms of these operators, we give a hierarchy of partition functions with <italic>W</italic>-representations and present their character expansions. Moreover, certain two <italic>&#946;</italic>-deformed integrals are constructed, where the measures are associated with the corresponding ground state wave functions of Hermite and Laguerre type CS models. We analyze the superintegrability property and show that these two integrals belong to the partition function hierarchy.

China

Fu-Hao Zhang

Fan Liu

Chun-Hong Zhang

Rui Wang

Superintegrability for two <italic>&#946;</italic>-deformed integrals

Astrophysical black holes (BHs) are inevitably surrounded by dark matter halos and plasma environments, yet most theoretical studies idealize them as isolated vacuum solutions. Bridging this gap requires understanding how non-Abelian gauge fields and dark matter jointly modify BH geometry, thermodynamics, and observational signatures—a challenge compounded by quantum gravitational effects that become crucial during late-stage evaporation. We investigate Yang-Mills (YM) charged BHs embedded in perfect fluid dark matter (PFDM) backgrounds, incorporating quantum corrections through the Generalized Uncertainty Principle (GUP) and Zitterbewegung oscillations. Starting from an action combining Einstein gravity, Maxwell electromagnetism, non-Abelian YM fields, and PFDM, we derive static spherically symmetric solutions with metric function <math altimg='si27.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>2</mn><mi>M</mi><mo linebreak='goodbreak'>/</mo><mi>r</mi><mo linebreak='goodbreak'>+</mo><msup><mi>Q</mi><mn>2</mn></msup><mo linebreak='goodbreak'>/</mo><msup><mi>r</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><msub><mi>Q</mi><mtext>YM</mtext></msub><mo linebreak='goodbreak'>/</mo><msup><mi>r</mi><mrow><mn>4</mn><mi>p</mi><mo>&#8722;</mo><mn>2</mn></mrow></msup><mo linebreak='goodbreak'>+</mo><mrow><mo>(</mo><mi>&#945;</mi><mo linebreak='badbreak'>/</mo><mi>r</mi><mo>)</mo></mrow><mi>ln</mi><mrow><mo>(</mo><mi>r</mi><mo linebreak='badbreak'>/</mo><mo>|</mo><mi>&#945;</mi><mo>|</mo><mo>)</mo></mrow></mrow></math>, where <italic>p</italic> controls YM self-interactions and <italic>&#945;</italic> governs dark matter coupling. Applying the Wentzel-Kramers-Brillouin (WKB) tunneling formalism, we compute spin-dependent Hawking temperatures, finding that higher-spin channels dominate emission, and GUP effects stabilize Planck-scale remnants. Exponential entropy corrections <math altimg='si28.svg'><mrow><msub><mi>S</mi><mi>C</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>S</mi><mn>0</mn></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mrow><mo>&#8722;</mo><msub><mi>S</mi><mn>0</mn></msub></mrow></msup></mrow></math> yield quantum-modified thermodynamic potentials exhibiting phase transitions, while Joule-Thomson analysis reveals intricate cooling-heating regimes with multiple inversion curves. Keplerian frequency calculations demonstrate how YM charges and PFDM shift the innermost stable circular orbit (ISCO), and photon sphere analysis in dispersive plasma determines frequency-dependent shadow radii.

Türkiye

İzzet Sakallı

Yusuf Sucu

Erdem Sucu

Zitterbewegung oscillations and GUP-induced quantum modifications of Yang-Mills black holes in perfect fluid dark matter

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>We investigate a classical model of coupled harmonic oscillators (CHO) as the classical counterpart of the Lee model. In this classical model, the divergence of the fundamental frequency and its renormalization precisely reproduce the divergence and renormalization of the physical mass of the particle, revealing that mass divergence in the Lee model is not solely a quantum phenomenon.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>We derive the necessary conditions that any renormalization must satisfy for the two-oscillator system corresponding to the single-mode Lee model.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>We examine the classical analog of the <italic>N</italic>-<italic>&#952;</italic> scattering process in the Lee model and demonstrate that the cutoff-dependent behavior of the scattering strength parallels the quantum scenario, indicating that the suppression of scattering also has a classical origin.</para></list-item></list>

Kang Xu

C.P. Sun

Classical analog of the T. D. Lee model for renormalization

We study interacting ultraviolet fixed points in a modified Litim-Sannino model with additional operators of dimension=4. This is a four-dimensional <italic>SU</italic>( <italic>N<inf>c</inf></italic>) quantum gauge theory coupled to <italic>N<inf>f</inf></italic> species of color fermions and <math altimg='si37.svg'><msubsup><mi>N</mi><mi>f</mi><mn>2</mn></msubsup></math> colorless scalars, which we study in the Veneziano limit. We investigate the case where the global flavor symmetry <italic>SU</italic>( <italic>N<inf>f</inf></italic>) <inf><italic>L</italic></inf>&#8239;&#215;&#8239; <italic>SU</italic>( <italic>N<inf>f</inf></italic>) <inf><italic>R</italic></inf> reduces to the diagonal flavor symmetry <italic>SU</italic>( <italic>N<inf>f</inf></italic>). This modification requires new Yukawa interactions and a rich structure of all possible quartic scalar operators. General expressions for the RGEs up to four loops in the gauge and three loops in the Yukawa and quartic couplings in the extended theory with operators of dimension=4 are determined. Fixed points, critical exponents and anomalous dimensions for fields, scalar mass squared, and a class of dimension-three operators are also provided.

"A.I." Mukhaeva

On asymptotic safety in 4D gauge theory with additional dimension=4 operators

The characteristics of compact stars are examined in this study utilizing the Kohler-Chao-Tikekar and Tolman IV spacetime models. This study is framed within the <italic>f</italic>( <italic>Q</italic>) gravity, a geometric theory of gravity where spacetime curvature is describe by the non-metricity, <italic>Q</italic>. The governing equations for the star&#8217;s interior, whose fluid composition is modeled by the perfect matter, are derived initially for a quadratic gravity model, which is predicated on a static, spherically symmetric spacetime. Considering both spacetimes separately results in two different new solutions. We apply boundary conditions at the star&#8217;s surface, necessitating continuity with the known Schwarzschild exterior line element, in order to identify the unknowns in our solutions. A thorough set of physical acceptance standards is then discussed in relation to the developed models to guarantee that the stellar models accurately depict compact objects. Using the well-constrained compact stars, such as LMC X-4 and Her X-1, as benchmark candidates, we perform a graphical analysis to verify the parameter space of our models in order to ground our theory in observation. Our findings show that, within a certain range of parameters, both stellar solutions are physically feasible. This work ultimately improves our knowledge of compact star interiors within symmetric teleparallel gravity by offering a solid theoretical framework and significant avenues for further research in this area.

Pakistan

Azerbaijan

Tayyab Naseer

M. Sharif

M. Waqas

Saudi Arabia

Jordan

Kottakkaran Sooppy Nisar

Mohammed Zakarya

Signatures of non-metricity on dynamical analysis of isotropic cosmological models

We investigate the astrophysical properties of the rotating Kazakov-Solodukhin (KS) black hole, a quantum-corrected extension of the Schwarzschild solution that removes the central singularity via an effective mass function. Extending the KS solution to the rotating case, we analyze its geodesic structure and explore the influence of the quantum correction parameter on observable quantities. In particular, we study the effective mass profile, the ergoregion, and photon motion, and compute the black hole shadow. Comparing the resulting shadows with the classical Kerr solution, we find that quantum corrections tend to enlarge the shadow radius and alter its shape. Using these theoretical predictions, we further constrain the parameter space of the rotating KS black hole by confronting the shadow properties with Event Horizon Telescope (EHT) observations of M87* and Sgr A*. Our results demonstrate that high-resolution black hole imaging provides a promising avenue for probing semiclassical modifications of general relativity.

Uzbekistan

Bekzod Rahmatov

Islom Egamberdiev

Otabek Umarov

Murodbek Vapayev

Shavkat Karshiboev

Yunus Turaev

Sardor Murodov

Astrophysical signatures of rotating Kazakov-Solodukhin black holes: shadows and constraints from EHT observations

The anisotropic distribution of ultra high energy cosmic rays (UHECRs) remains a compelling and deeply informative observable in astro-particle physics, illuminating their enigmatic origins, extreme acceleration processes, and trajectories shaped by the cosmic large-scale structure. Among the hierarchy of anisotropy modes, the dipole stands out as a particularly sensitive tracer reflecting both the spatial configuration of sources and the foundational cosmological model. In this work, we conduct a rigorous comparative analysis of dipolar anisotropy within the diffusive propagation regime, evaluating its evolution across three gravitational framework: the standard ΛCDM model, a power-law extension of <italic>f</italic>( <italic>R</italic>) modified gravity, and the Starobinsky inflationary scenario. Our objective is to disentangle the gravitational signatures embedded in UHECR anisotropy, with particular emphasis on deviations arising from extended theories of gravity within the <italic>f</italic>( <italic>R</italic>) formalism. The results reveal a striking dependence on the underlying gravitational paradigm: the power-law model predicts significantly enhanced anisotropies, &#923;CDM consistently produces the most suppressed amplitudes, and the Starobinsky model exhibits an intermediate profile with partial convergence toward &#923;CDM. These findings reinforce the notion that UHECR anisotropy is not merely a reflection of astrophysical processes, but also a subtle messenger of the fundamental gravitational laws governing the universe offering a novel and promising avenue for testing physics beyond the standard cosmological framework.

Iftikhar Ahmad

Muhammad Mahtisham

Adnan Malik

Fatemah Mofarreh

Model-dependent predictions for UHECR dipolar anisotropies in a <italic>f</italic>( <italic>R</italic>) modified gravity

General Relativity (GR) is not the only way gravity can be geometrized. Instead of curvature, the Teleparallel Theory attributes gravity to the torsion <italic>T</italic>, which is related to the antisymmetric part of the connection. On the other hand, the Symmetric Teleparallel Theory no longer preserves metricity, describing gravity through the non-metricity tensor <italic>Q<inf>&#945;&#956;&#957;</inf></italic>&#8239;&#8801;&#8239;&#8711; <inf><italic>&#945;</italic></inf> <italic>g<inf>&#956;&#957;</inf></italic>. These descriptions give form to what is known as geometrical trinity of gravity. Recently, the extensions of GR have been intensively investigated in order to solve the theoretical impasses which have arisen. In this sense, it is also useful to investigate the extensions of alternative descriptions of gravity, which leads us to the so-called <italic>f</italic>( <italic>T</italic>) and <italic>f</italic>( <italic>Q</italic>) gravities. In this paper, we consider a family of <italic>f</italic>( <italic>Q</italic>) models and obtain their corresponding Tolman-Oppenheimer-Volkoff equations applied to polytropic stars. It is worth mentioning that the <italic>f</italic>( <italic>Q</italic>) covariant formulation is adopted and we present a new equation that substantially simplifies the numerical calculations. Using numerical integration, it is possible to solve a system of differential equations to calculate, among other things, the maximum mass and mass-radius relation allowed. In addition, we explicitly show the non-metricity behavior inside and outside the star.

Brazil

J.C.N. de Araujo

H.G.M. Fortes

Polytropic stars in <math altimg='si11.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#958;</mi><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> covariant formulation

In the context of fitting cosmological models, parameter degeneracy remains a central issue. This paper critically examines traditional methods for constraining parameters and focuses on the <italic>G</italic> factor as a tool for evaluating the quality of observational data. To ensure analytical independence, two datasets-Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO)-were utilized as samples for parameter fitting, supplemented by Markov Chain Monte Carlo (MCMC) simulations. The Figure of Merit (FoM) matrix served as the final criterion for assessing fitting performance. The results show that the <italic>G</italic> factor of the CC dataset increases linearly with redshift <italic>z</italic>, whereas the <italic>G</italic> factor of the BAO dataset follows a cubic relationship. Further analysis indicates that the FoM value for datasets with high <italic>G</italic> factors is significantly higher than that for datasets with low <italic>G</italic> factors, thereby validating the <italic>G</italic> factor&#8217;s effectiveness as a tool for assessing observational data quality and reducing parameter degeneracy. This suggests that the <italic>G</italic> factor may serve as a diagnostic tool and selection criterion for optimizing observational datasets in future research.

Yuan-Bo Xie

Yun-Dong Wu

Wei Hong

Tong-Jie Zhang

Exploring the cosmological model degeneracy with a new evaluate factor <italic>G</italic>