In the present article, we introduce $\textit{Q}$-solitons, a generalization of Riemann solitons, on (almost) coKähler manifolds ( , in short). Here we obtain a necessary condition from which we establish that a compact admitting $\textit{Q}$-soliton whose soliton vector field is pointwise collinear with the Reeb vector field is a $\textit{K}$- . We also prove that the soliton vector field of a $\textit{Q}$-soliton on $$(\kappa ,\mu )$$ - with $$\kappa <0$$ is an infinitesimal contact transformation. For the gradient case, we show that under certain restriction a $$(\kappa ,\mu )$$ - $$(\kappa <0)$$ reduces to $\textit{N}$($\textit{K}$)- . We deduce that a three dimensional coKähler manifold admitting $\textit{Q}$-soliton obeys $$\Delta \mathfrak {R}+\Delta \Psi =0$$ . Also we construct an example to verify our deduced results. Moreover, we explore certain results on $\textit{Q}$-solitons in the context of relativistic magneto-fluid spacetimes.

India

Gaurab Mitra

Avijit Sarkar

Tarak Mandal

Characterizations of $\textit{Q}$-solitons on (almost) coKähler manifolds and its applications in magneto-fluid spacetimes

We systematically investigate static plane symmetric configurations in $\textit{f}$($\textit{Q}$) gravity. For vacuum regions, we discuss the constancy of the nonmetricity scalar $\textit{Q}$ and derive general vacuum solutions, which correspond effectively to Taub-(anti) de Sitter spacetimes with a cosmological constant determined by the specific $\textit{f}$($\textit{Q}$) model. By matching a singular thin shell source to the vacuum solutions, we relate the shell’s energy density and pressure to the integration constants of the exterior geometry. We also examine a finite-thickness slab as another matter source supporting the vacuum solution. Through numerical analysis of a quadratic model $$f(Q)=Q+\alpha Q^2$$ with isotropic matter, we show that the maximum pressure inside the slab generally does not coincide with the geometric center. Moreover, a negative $$\alpha $$ with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive $$\alpha $$ are incompatible with a self-gravitating slab of positive pressure.

China

Jun-Qin Long

Rui-Hui Lin

Xiang-Hua Zhai

Static plane symmetric solutions in $\textit{f}$($\textit{Q}$) gravity

We investigate the consistency of linear dark sector interactions within coincident <italic>f</italic>( <italic>Q</italic>) gravity restricting to a &#923;CDM-mimicking background. We focus on a linear model supplemented by a geometrically motivated background-inert <math altimg='si23.svg'><msqrt><mi>Q</mi></msqrt></math> correction ensuring expansion history identical to &#923;CDM, with all the gravitationally motivated effects arising exclusively at the perturbation level. We show that background consistency enforces a nontrivial structural restriction - any interaction proportional to the matter density is mathematically incompatible leading to a unique dark energy proportional coupling. This unique no-go result reflects the geometric origin of the effective dark energy sector in <italic>f</italic>( <italic>Q</italic>) gravity. The parameter space of this residual interacting sector is quantified using Markov Chain Monte Carlo analysis using late-time cosmological data including Redshift-Space Distortions, updated Cosmic Chronometers, DESI DR2 BAO and Type Ia Supernovae. The <math altimg='si23.svg'><msqrt><mi>Q</mi></msqrt></math> term modifies growth structure through a gravitational coupling, introducing perturbation level sensitivity in <italic>f&#963;</italic> <inf>8</inf>. We find that all the parameters are tightly constrained and are compatible with zero, indicating the strong observational limits on perturbation level departures from &#923;CDM. The model remains statistically compatible with &#923;CDM according to information criteria, while preserving a viable growth history. Our results therefore establish sharp structural and observational bounds on interacting dark energy scenarios in Symmetric Teleparallel Gravity, providing a benchmark consistency test for future high precision surveys.

Ameya Kolhatkar

Preet Dalal

P.K. Sahoo

Structural constraints on interacting dark sector in ΛCDM-mimicking <italic>f</italic>( <italic>Q</italic>) gravity

We investigate static black hole solutions in three-dimensional <math altimg='si1.svg'><mrow><mo>(</mo><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math> spacetime within the framework of modified <italic>F</italic>( <italic>Q, T</italic>) gravity, where the gravitational action depends on the non-metricity scalar <italic>Q</italic> and the trace of the energy-momentum tensor <italic>T</italic>. Considering a linear model <math altimg='si11.svg'><mrow><mi>F</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>C</mi><mn>1</mn></msub><mi>Q</mi><mo linebreak='goodbreak'>+</mo><msub><mi>C</mi><mn>2</mn></msub><mi>T</mi></mrow></math>, we derive the modified field equations under a Schwarzschild-like gauge and obtain both perturbative and numerical solutions. The weak-field expansion is shown to be valid in the asymptotic regime | <italic>a</italic>( <italic>r</italic>)|&#8239;&#8810;&#8239;1, while the near-horizon structure is analyzed through full numerical integration of the coupled differential system. The horizon is defined consistently in <math altimg='si12.svg'><mrow><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn></mrow></math> dimensions via <math altimg='si4.svg'><mrow><mi>A</mi><mo>(</mo><msub><mi>r</mi><mo>+</mo></msub><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math>, and the Hawking temperature is obtained from surface gravity without invoking four-dimensional Schwarzschild relations. Using the Wald formalism adapted to non-metricity gravity, we derive the entropy and show that it reduces to <math altimg='si13.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mi>&#960;</mi><msub><mi>C</mi><mn>1</mn></msub><msub><mi>r</mi><mo>+</mo></msub><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math>, recovering the BTZ result in the limit <math altimg='si14.svg'><mrow><msub><mi>C</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>. A general expression for the heat capacity is obtained, demonstrating that its sign depends on the second radial derivative of the metric function. While BTZ-like geometries yield positive heat capacity and thermodynamic stability, the numerical <italic>F</italic>( <italic>Q, T</italic>) solutions exhibit regions where <math altimg='si15.svg'><mrow><msup><mi>A</mi><mrow><mo>&#8243;</mo></mrow></msup><mrow><mo>(</mo><msub><mi>r</mi><mo>+</mo></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>&lt;</mo><mn>0</mn></mrow></math>, leading to negative heat capacity and instability. Our results show that although the leading-order horizon structure coincides with BTZ geometry, the matter non-metricity coupling significantly modifies the radial structure and thermodynamic stability. This demonstrates that <italic>F</italic>( <italic>Q, T</italic>) gravity in three dimensions admits black hole solutions that are geometrically BTZ-like but thermodynamically distinct.

Iran

S. Davood Sadatian

S. Mohamad Reza Hosseini

Black hole solutions in three-dimensional gravity within the framework of the modified <italic>F</italic>( <italic>Q, T</italic>) gravity model

We investigate the cosmological implications of two analytically solvable <italic>f</italic>( <italic>Q</italic>) gravity models within the framework of symmetric teleparallel gravity. The first model corresponds to the linear case <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>=</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi></mrow></math>, which is dynamically equivalent to general relativity with a cosmological constant, while the second model introduces a nonlinear correction <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>=</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi><mo linebreak='goodbreak'>/</mo><mi>Q</mi></mrow></math>. By assuming pressureless matter, we derive exact background solutions for both models, allowing the Hubble expansion rate, the matter energy density, and the deceleration parameter to be expressed in terms of the redshift. Then, we constrain the model parameters using a Bayesian Markov Chain Monte Carlo analysis based on <italic>H</italic>( <italic>z</italic>) cosmic chronometer measurements, the Pantheon+SH0ES Type Ia supernova compilation, and DESI baryon acoustic oscillation data. The results show that the linear model reproduces the standard &#923;CDM background dynamics, whereas the nonlinear model leads to modified cosmological evolution while remaining consistent with observational data. Moreover, the reconstructed deceleration parameter indicates a transition from an early matter-dominated decelerating phase to the present accelerated expansion. In addition, the <italic>Om</italic>( <italic>z</italic>) diagnostic reveals that Model I behaves identically to &#923;CDM, while Model II exhibits a redshift-dependent behavior indicative of a phantom-like effective regime. We conclude that symmetric teleparallel <italic>f</italic>( <italic>Q</italic>) gravity presents a viable geometric framework for describing the late-time acceleration of the universe.

Morocco

M. Koussour

Saudi Arabia

Alnadhief H.A. Alfedeel

Uzbekistan

I. Davletov

J. Rayimbaev

Matching exact cosmological solutions in linear and nonlinear <italic>f</italic>( <italic>Q</italic>) gravity with cosmological data

It was recently discovered that waves scattering off a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> ball can extract energy from it. We present an analytical treatment of this process by adopting a multistep function approximation for the background field, which yields perturbative solutions expressed in terms of Bessel functions. For thin-wall <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> balls, the amplification factors reduce to simple sinusoidal functions, which explains the multipeak structure of the spectrum and identifies the physical quantities that determine it. For instance, at high frequencies, the peak spacing is simply the inverse of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball size. The analytical solution further enables us to delineate the full range of possible amplification factors. For general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> balls, this analytical framework also substantially improves the efficiency of evaluating the amplification factors.

Guo-Dong Zhang

Shuang-Yong Zhou

Meng-Fan Zhu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball superradiance: Analytical approach

This article explores traversable wormhole geometries obtained in the context of the symmetric teleparallel gravity theory and highlights their distinctive physical characteristics. Our methodology involves determining the tidal force by employing a specified form of the shape function along with an appropriate equation of state for Case I. In order to extract the shape functions associated with the wormhole solution, we apply the null-complexity condition with tidal force in Case II. In Case III, we utilize the balancing Tolman–Oppenheimer–Volkoff equation in conjunction with a tidal force to obtain viable wormhole shape function. The analysis focuses on the dependence of wormhole characteristics on the parameter $$\zeta $$ . The energy conditions are examined within their respective validity domains for various ranges of the model parameters. We also calculate, the volume integral quantifier, the extent of exotic matter needed to uphold the traversable wormhole structure. Through the effective potential for timelike geodesics, the influence of angular momentum on trajectories is clarified, and the corresponding deflection angle evaluation points to significant light bending close to the throat. By introducing small radial perturbations around the equilibrium shell radius, we examine the stability characteristics for all considered shape functions.

Sweeti Kiroriwal

Oman

Azerbaijan

S. Maurya

Jitendra Kumar

Wormhole solutions under tidal force constraints in $\textit{f}$($\textit{Q}$) gravity: a unified approach

The study of nuclear modification factor is crucial in advancing our knowledge of the hot and dense nuclear matter created during high energy heavy-ion collision. In this direction, we have developed a theoretical model for the nuclear modification factor using the Boltzmann transport equation in relaxation time approximation with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-Weibull distribution as the final state distribution and studied the experimental data of nuclear modification factor of charged hadrons as well as identified particles at various energies ranging from 7.7 GeV measured at RHIC up to the maximum value of 5.44 TeV studied in LHC. We observed a good agreement between the model and the experimental data as can be quantified using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup><mo>/</mo><mi>N</mi><mi>D</mi><mi>F</mi></math> values. We have also studied the mass dependence of different fit parameters that appears in the theoretical model and observe a linear mass dependence of some parameters.

Rohit Gupta

Investigation of the nuclear modification factor from RHIC to LHC energies using the Boltzmann transport equation in conjunction with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-Weibull distribution

The Local Unitarity (LU) formalism provides a constructive, integrand-level realisation of the Kinoshita-Lee-Nauenberg (KLN) theorem, by combining loop and phase-space integrals appearing in scattering cross-sections in such a way that their final-state infrared singularities cancel before integration. Supplemented with localised ultraviolet renormalisation, it enables the direct Monte Carlo integration of cross sections at arbitrary perturbative order in four-dimensional spacetime. In this paper, we present its application to the next-to-next-to-leading order (NNLO) QCD total cross sections for heavy-quark pair production in direct photon fusion, involving the contribution from 138 distinct forward-scattering diagrams where external photons couple only to heavy quarks. By combining NNLO QCD with next-to-leading order (NLO) electroweak (EW) corrections and next-to-leading power (NLP) Coulomb resummation, we obtain state-of-the-art predictions for top-, bottom-, and charm-quark production in ultraperipheral hadron collisions and at $\textit{e}$ $\textit{e}$ colliders.

Switzerland

Zeno Capatti

Mathijs Fraaije

Valentin Hirschi

Lucien Huber

Ben Ruijl

France

Hua-Sheng Shao

NNLO QCD corrections to $\textit{γγ}$ → $$ Q\overline{Q} $$ from Local Unitarity combined with Coulomb resummation and NLO EW effects

The method of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math> cumulants has been shown as a powerful tool to study the fine details of the azimuthal anisotropies in high-energy nucleus-nucleus collisions. A new method for the fast calculation of arbitrary order <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math>-cumulant <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mi>n</mi></msub><mrow><mo>{</mo><mn>2</mn><mi>k</mi><mo>}</mo></mrow></mrow></math> values, based on the partition of a non-negative integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>l</mi><mo>≤</mo><mi>m</mi></mrow></math> for calculation of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>m</mi></mrow></math>-particle azimuthal correlations is presented in this paper. Unlike the standard <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math>-cumulants method in which the calculation of high-order multiparticle calculations is impractical, the newly proposed method enables easy calculation. The validity of the method is proven via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles. The method enables the study of fine details of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> distribution, such as higher-order central moments of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> distribution, as well as the hydrodynamic behavior of the quark-gluon plasma.

Serbia

L. Nađđerđ

J. Milošević

D. Devetak

United States

F. Wang

X. Zhu

Novel approach to a fast calculation of high-order <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math> cumulants