We investigate the velocity-dependent one-scale model to the case of one cosmic F-string and two D-strings as color flux tubes in pure Spin(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>N</mi></math>) gauge theory. We analytically calculate the scaling string density as a function of the reconnection probabilities, and confirm our results with numerical calculations. We also determine the timescale at which the string density reaches the scaling regime, and find that for certain values of the reconnection probability, the scaling time can become extremely large, by many orders of magnitude. This leads to a characteristic suppression signature of the gravitational-wave signal at high frequencies, which may become observable in the frequency range of future interferometric gravitational-wave observations.

Japan

Kazuto Nakamura

Masaki Yamada

Delayed scaling of multitype cosmic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-strings in velocity-dependent one-scale models

In this work, we investigate exact black string solutions in the context of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity. Adopting the specific form $$f(R,T) = R + 2\chi T$$ , we consider an anisotropic Kiselev fluid as the matter content and obtain static cylindrical solutions, which are then extended to the rotating case through a suitable coordinate transformation. The influence of the quintessence state parameter $$w_q$$ and the matter–geometry coupling constant $$\chi $$ on the geometry is analyzed. We examine the weak, null, and strong energy conditions, identifying the regions in the parameter space where they are satisfied. Furthermore, we apply the Hamilton–Jacobi method to study the tunneling of scalar particles across the event horizon and derive the corresponding Hawking temperature. The thermodynamic stability of the solutions is investigated by computing the heat capacity, and the conditions for phase transitions are discussed. The results provide a characterization of black strings in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity surrounded by quintessence, highlighting the combined effects of anisotropic matter and modified gravity on their physical properties.

Brazil

L. Santos

L. Barbosa

C. Barros

Kiselev black strings in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity

This research paper explores the structure of hypothetical compact stars, known as strange stars, within the framework of a novel modified theory of gravity called $$f(R,\Sigma ,T)$$ gravity. This theory extends General Relativity by making gravity dependent not only on the Ricci curvature scalar $\textit{R}$ but also on a torsion scalar $$\Sigma $$ and the trace of the matter energy–momentum tensor $\textit{T}$. This introduces a richer coupling between geometry and matter. The study presents a highly exotic, multi-layered stellar model composed of five distinct regions, each with a unique equation of state and geometric properties. The model features a dark-energy-like core with powerful repulsive gravity (anti-gravity), surrounded by successive layers of dust, exotic radiation, and a stiff matter crust, all enveloped by a standard Schwarzschild vacuum exterior. A key finding is the prevalence of negative energy densities and pressures in several layers, a hallmark of exotic matter. These configurations, enabled by the $$f(R,\Sigma ,T)$$ framework, lead to repulsive gravitational effects that radically alter the star’s internal equilibrium. The analysis demonstrates how additional geometry-driven forces within this theory can support such exotic structures, potentially preventing gravitational collapse and resulting in a stable, non-singular object. This work demonstrates that $$f(R,\Sigma ,T)$$ gravity allows for new and complex classes of compact objects with stratified, exotic matter distributions, whose properties and observational signatures would differ significantly from those predicted by standard General Relativity.

Egypt

M. Bakry

Saudi Arabia

A. Eid

Tahia Dabash

The impact of $$f(R,\Sigma ,T)$$ gravity on strange star structure

In this study, we analyze $\textit{f}$($\textit{R}$) gravity employing the $$ f(R) = R+ \alpha _1 R^p - \alpha _2 R^{-q} $$ model within the Friedmann–Lemaître–Robertson–Walker (FLRW) background. We derive the Friedmann equations via modified gravity action and subsequently reexpress them in terms of the standard Friedmann equations. Our investigation explores the behavior of a bouncing cosmological model within this modified gravity context, offering a potential solution to the singularity problem encountered in the standard Big Bang cosmology. We represent cosmological parameters as functions of cosmic time and scrutinize the conditions for a cosmic bounce. Additionally, we reconstruct the $\textit{f}$($\textit{R}$) gravity model using the redshift parameter and graphically present cosmological parameters as functions of redshift. These plots reveal an accelerated nature of Universe expansion. Furthermore, we reconstruct $\textit{f}$($\textit{R}$) gravity models for scale factors, $$a(t) = e^{e^{\lambda t}}$$ which exhibits the bouncing behavior. Finally, we investigated the stability scenario by examining the sound speed. The resulting graph of sound speed plotted against redshift confirms late-time stability.

Pakistan

M. Ilyas

Khalid Masood

South Korea

Nehad Shah

Dynamical analysis of bouncing cosmology in the Capozziello–De Laurentis model of $\textit{f}$($\textit{R}$) gravity

Tensor-polarized twist-3 parton distribution functions (PDFs) <italic>f<inf>LT</inf></italic>( <italic>x</italic>) are calculated for the spin-1 deuteron by using twist-2 relations, which are similar to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule in the spin-1/2 nucleon, together with tensor-polarized twist-2 PDFs <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). The PDFs are shown for <italic>f<inf>LT</inf></italic>( <italic>x</italic>) at <math altimg='si1.svg'><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mn>2.5</mn></mrow></math>&#8239;GeV 2, where the tensor-polarized PDFs <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>) are provided. The <italic>x</italic>-dependence of <italic>f<inf>LT</inf></italic>( <italic>x</italic>) is similar to <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>), and the magnitude of <italic>f<inf>LT</inf></italic>( <italic>x</italic>) is roughly of the order of <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). In experiments at the Thomas Jefferson National Accelerator Facility (JLab), higher-twist effects could be sizable because <italic>Q</italic> 2 values are not very large in comparison with the hadronic scale of 1&#8239;GeV 2. Therefore, the JLab experiments could provide a good opportunity to investigate the twist-3 distributions <italic>f<inf>LT</inf></italic>( <italic>x</italic>) in addition to the twist-2 ones <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). Furthermore, these tensor-polarized PDFs could be investigated at future Electron-Ion Colliders (EICs) and hadron accelerator facilities such as the Fermi National Accelerator Laboratory (Fermilab), the Nuclotron-based Ion Collider fAcility (NICA), and the Large Hadron Collider (LHC).

China

S. Kumano

Kenshi Kuroki

Tensor-polarized twist-3 parton distribution functions <italic>f<inf>LT</inf></italic>( <italic>x</italic>) for the spin-1 deuteron by using twist-2 relations

The aim of this paper is to investigate the stability and existence of the closed Einstein Universe (EU) under linear homogeneous perturbations within the framework of $$ f(\mathcal {R}, \phi , \chi ) $$ gravity. For this, we consider a closed Friedmann–Roberson–Walker universe filled with isotropic matter. Perturbations are imposed on the matter parameters and on the scale factor. We systematically derive the static and perturbed field equations for scenarios with and without conservation of the energy–momentum tensor and examine the associated stability regions through selected models in $$f(\mathcal {R},\phi ,\chi )$$ gravity. The graphical analysis shows that for suitable choices of model parameters such as $$ \alpha $$ , $\textit{b}$ and scalar field $$\phi _o$$ , the stable regions of the Einstein universe can be obtained in this theory of gravity. Significant differences in stability regions are observed for scalar fields governed by standard kinetic energy and for those characterized by negative kinetic energy. The scalar field and coupling parameters play a key role in the existence of stable regions of the Einstein universe.

 Muhammad

M. Azam

A perturbative approach on the stability of the Einstein universe in $$f(\mathcal {R},\phi ,\chi )$$ gravity

In this work, we explore the formulation of the Misner-Sharp energy within the framework of <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>)</mo></mrow></math> gravity, a modified theory incorporating the Ricci scalar <italic>R</italic> and the Gauss-Bonnet scalar <math altimg='si4.svg'><mi mathvariant='script'>G</mi></math>. By extending the quasilocal energy definition to both static spherically symmetric spacetime and the dynamic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive explicit expressions for the generalized Misner-Sharp energy using two complementary approaches: the integration method and the conserved charge method based on the Kodama vector. Our analysis shows that the Misner-Sharp energy expression in <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>)</mo></mrow></math> gravity reduces to standard <italic>f</italic>( <italic>R</italic>) gravity results when the Gauss-Bonnet term is absent, revealing how curvature modifications influence the geometric structure and dynamics of cosmic evolution. Furthermore, we investigate the thermodynamic properties at the apparent horizon associated with the FLRW background, and we find a connection to non-equilibrium thermodynamics unique to <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>)</mo></mrow></math> gravity. These findings underscore the subtle and fundamental role of curvature corrections in determining the energy distribution and thermodynamic behavior of gravitational systems.

Iran

Türkiye

Amin Rezaei Akbarieh

Navid Safarzadeh Ilkhchi

Yaghoub Heydarzade

Generalized Misner-Sharp energy in <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>)</mo></mrow></math> gravity

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory <math altimg='si3.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>T</mi><msub><mi>L</mi><mi>m</mi></msub></mrow></math>, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: <math altimg='si9.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si6.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>. We show that the extra <italic>&#945;TL<inf>m</inf></italic> term significantly alters the mass-radius relation of WDs, especially at high central densities <math altimg='si11.svg'><mrow><mo>(</mo><msub><mi>&#961;</mi><mi>c</mi></msub><mo>&#8819;</mo><msup><mn>10</mn><mn>8</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><msup><mn>10</mn><mn>9</mn></msup><mspace width='0.16em' /><mrow><mi mathvariant='normal'>g</mi></mrow><mo linebreak='goodbreak'>/</mo><mi>c</mi><msup><mi>m</mi><mn>3</mn></msup><mo>)</mo></mrow></math>, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter <italic>&#945;</italic>, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter <italic>&#945;</italic> for the two choices of the Lagrangian density <italic>L<inf>m</inf></italic>.

Edson Otoniel

Juan M.Z. Pretel

Clésio E. Mota

César O.V. Flores

Victor B.T. Alves

Germany

Franciele M. da Silva

White dwarf structure in <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity: Beyond the Chandrasekhar mass limit

We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 –10 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.

United States

Washington Taylor

Yi-Nan Wang

Yihang Yu

Statistics of base polytopes in F-theory

In this work, we examine the influence of nonlinear electrodynamics (NED) and <italic>f</italic>( <italic>R, T</italic>) gravity on quasi-periodic oscillations (QPOs) around a magnetically charged black hole. By analyzing the effective potential, specific energy, and angular momentum of circular orbits, we study how the NED parameter <italic>&#945;</italic> and the gravitational coupling parameter <italic>&#946;</italic> affect orbital dynamics. Increasing <italic>&#945;</italic> leads to systematic deviations from the Reissner-Nordstr&#246;m behavior, reflected in shifts in the ISCO radius and orbital frequencies. We further explore QPO-generating radii using the Relativistic Precession (RP), Warped Disk (WD), and Epicyclic Resonance (ER2-ER4) models. We further extend our analysis by performing an MCMC-based parameter estimation using QPO data from black holes spanning a wide range of mass scales. This approach yields consistent observational constraints on the model parameters.

India

Bidyut Hazarika

Abhishek Baruah

Prabwal Phukon

Observational constraints on <italic>f</italic>( <italic>R, T</italic>) gravity coupled with NED from black hole quasi periodic oscillations