Egypt

Tahia Dabash

United States

Moataz Emam

Germany

Lukas Schöppner

Reply to “Comment on: Symmetry and conserved quantities in $\textit{f}$($\textit{R}$)-gravity: Mei vs. Noether approaches”

In this work, two analytical solutions are proposed to characterize compact star configurations containing an effective negative-pressure fluid in the <italic>f</italic>( <italic>R, T</italic>) gravity paradigm that admit spherically symmetric geometry. We derive a system of modified field equations by taking into account a static interior spacetime, which consists of both negative-pressure fluid and ordinary matter sources. In order to investigate the interactions between the fluid components, we solve the field equations using two different equations of state. As the gravitational equations still contain more unknowns, we further use the Finch-Skea and Tolman IV spacetimes which lead us to two distinct models. The junction conditions are also applied to compute the constants associated with these solutions. Afterwards, our developed models&#8217; feasibility is explored by contrasting them with the observed characteristics of two particular stars, SAX J1808.4&#8211;3658 and Her X-1. Under certain parametric values, our results demonstrate that both the developed fluid configurations are physically realistic in this minimally coupled gravity framework.

Azerbaijan

Pakistan

M. Sharif

Tayyab Naseer

Aqsa Bashir

Examining the behavior of exotic compact stars within the <italic>f</italic>( <italic>R, T</italic>) gravity under Finch-Skea and Tolman IV spacetimes

Using the $$C-$$ metric in the context of $\textit{F}$($\textit{R}$) gravity coupled with the ModMax nonlinear electromagnetic field (the $$F(R)-$$ ModMax theory), we derive an exact black hole solution in a four-dimensional spacetime. We then examine how various parameters influence the behavior of accelerating ModMax black holes. Treating this black hole as a thermodynamic system, we calculate the Hawking temperature and entropy for the accelerating ModMax black holes within the framework of $\textit{F}$($\textit{R}$) gravity. Subsequently, we explore the impact of the parameters in $$F(R)-$$ ModMax theory on the Hawking temperature and entropy. We also assess local stability by analyzing the heat capacity. Additionally, we investigate both the angular shadow and the shadow radius of an accelerating black hole in the context of $$F(R)-$$ ModMax gravity.

Iran

B. Panah

N. Heidari

Chile

Czechia

Á. Rincón

Accelerating electrically charged ModMax black hole solutions in $\textit{F}$($\textit{R}$) gravity

In this work, Static wormhole models are examined within the framework of curvature-based <math altimg='si17.svg'><mrow><mi mathvariant='italic'>f</mi><mo>(</mo><mi mathvariant='fraktur'>R</mi><mo>,</mo><msub><mi mathvariant='fraktur'>L</mi><mi mathvariant='fraktur'>m</mi></msub><mo>,</mo><mi mathvariant='italic'>T</mi><mo>)</mo></mrow></math> gravity theory. A relationship between the matter energy density and pressure is proposed for the Morris-Thorne wormhole geometry with a constant redshift function. By incorporating a gradient-dependent equation of state ( <math altimg='si18.svg'><mrow><msub><mi>P</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>P</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>&#961;</mi><mo>,</mo><msup><mi>&#961;</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> and <math altimg='si19.svg'><mrow><msub><mi>P</mi><mi>t</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>P</mi><mi>t</mi></msub><mrow><mo>(</mo><msub><mi>P</mi><mi>r</mi></msub><mo>,</mo><msubsup><mi>P</mi><mi>r</mi><mo>&#8242;</mo></msubsup><mo>)</mo></mrow></mrow></math>), we derive exact wormhole solutions for two representative cases. Our analysis shows that exact wormhole models can admit null energy condition violations localized at the throat, while preserving a non-negative matter energy density. The stability analysis is performed via the Tolman&#8211;Oppenheimer-Volkoff equation under hydrostatic equilibrium, demonstrating that the balance among anisotropic and hydrostatic forces sustains the wormhole&#8217;s stable configuration. For positive and negative values of <italic>&#950;</italic>, the energy flux attains a pronounced negative magnitude, inducing an outward flux that supports the stability of the wormhole throat. The geometric characteristics of the wormhole are examined through embedding diagrams, and the total exotic matter required to maintain the configuration is evaluated using the volume integral quantifier. Simultaneously, the effective potential demonstrates enhanced photon confinement and increased stability of particle orbits.

India

Sweeti Kiroriwal

Oman

S.K. Maurya

Jitendra Kumar

Wormholes generated by a density-gradient dependent equation of state in <math altimg='si17.svg'><mrow><mi mathvariant='italic'>f</mi><mo>(</mo><mi mathvariant='fraktur'>R</mi><mo>,</mo><msub><mi mathvariant='fraktur'>L</mi><mi mathvariant='fraktur'>m</mi></msub><mo>,</mo><mi mathvariant='italic'>T</mi><mo>)</mo></mrow></math> gravity

We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $\textit{f}$($\textit{R}$) model $$f(R)=R+\alpha R^2$$ . We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $$\alpha $$ . For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. We then use these results to infer the expected trend in the PBH formation threshold $$\delta _c$$ , rather than a direct quantitative determination. Within this perturbative framework, the quadratic correction modifies the dust collapse dynamics at first order, while the flat radiation-dominated background does not receive a nontrivial correction at the same order. As result, any modification of PBH formation in the radiation era must arise from nonlinear or non-perturbative effects. The perturbative analysis therefore provides qualitative insight into how curvature corrections influence collapse, particularly in high-curvature regimes. To access this regime we reformulate the theory in the Einstein frame, where the model becomes GR plus the scalaron field $$\phi $$ with the Starobinsky potential. We provide the complete ODE system governing both the cosmological background and the evolution of an overdense closed FLRW patch. This system can be numerically integrated to obtain the critical overdensity $$\delta _c(k)$$ for PBH formation near the end of inflation.

G. Nashed

Saudi Arabia

A. Eid

Primordial black hole formation in $$f(R)=R+\alpha R^2$$ gravity: perturbative and non-perturbative analysis

We constrain the Hu–Sawicki and Starobinsky $\textit{f}$($\textit{R}$) gravity models utilizing current electromagnetic (PantheonPlus + cosmic chronometers [PP+CC], Planck, and DESI2) datasets and simulate standard siren (SS) catalogs based on the resulting best-fit parameters. We demonstrate that the simulated SS data provide complementary sensitivity to the modified gravitational wave propagation friction term, thereby enhancing the discriminating power between $\textit{f}$($\textit{R}$) gravity and the $$\varLambda $$ CDM model. However, we note that standard sirens do not offer a viable resolution to the Hubble tension in this analysis, as the inferred constraints are predominantly driven by the fiducial cosmologies adopted in the simulations. Regarding the specific models, we find that for the Hu–Sawicki scenario, several data combinations favor $$F_{RR0}<0$$ , implying potential theoretical instabilities. And, for the Starobinsky model, while electromagnetic-only constraints are nearly symmetric between the two parameter branches ( $$b<0$$ and $$b>0$$ ), the inclusion of SS constraints introduces mild asymmetries, revealing the sensitivity of SS observables to the curvature dependence of the theory. Future truly independent standard siren observations would be crucial for a definitive assessment of $\textit{f}$($\textit{R}$) gravity as an alternative to $$\varLambda $$ CDM.

China

Yi Zhang

Xuanjun Niu

Xianfu Su

Dong-Ze He

The standard siren tests of viable $\textit{f}$($\textit{R}$) cosmologies

The present study analyzes anisotropic compact objects coupled with the electromagnetic field within the context of <italic>f</italic>( <italic>R, T</italic>) gravity. We obtain two novel solutions of modified field equations for a static charged spacetime. To simplify the system, we employ two different assumptions for the radial metric component and specific anisotropic pressure profiles, and obtain exact analytical solutions. The governing field equations in both models yield differential equations whose general solutions contain undetermined constants. These constants are evaluated through the junction conditions between the interior and the exterior Reissner-Nordstr&#246;m spacetimes across the boundary surface. In this regard, we also impose the condition that the radial pressure drops to zero on the star&#8217;s interface. Furthermore, we examine the fundamental prerequisites that must be fulfilled for physical existence of compact objects. For graphical analysis, we consider the observed data of two stars, LMC X-4 and SMC X-4, together with multiple parametric values. Our findings demonstrate that both resulting solutions satisfy the essential physical requirements under the considered modified gravitational framework for certain values of the charge and model parameter.

Hira Shadab

Role of electric charge in the construction of relativistic stellar solutions in <italic>f</italic>( <italic>R, T</italic>) gravity

The <italic>f</italic>( <italic>R, T</italic>) theory of gravity extends general relativity (GR) by allowing the gravitational Lagrangian to depend on both the Ricci scalar <italic>R</italic> and the trace of the energy-momentum tensor <italic>T</italic>. The resulting matter-geometry coupling introduces additional dynamical effects that may account for the late-time acceleration of the universe without invoking dark energy. In the present work, we focus instead on the early-time regime and investigate the corresponding quantum cosmological dynamics. We analyze a Friedmann&#8211;Lemaitre&#8211;Robertson&#8211;Walker (FLRW) universe within the <italic>f</italic>( <italic>R, T</italic>) framework, employing Schutz&#8217;s perfect fluid formalism to extract a time parameter emerging from the matter sector itself. This approach is particularly well motivated in <italic>f</italic>( <italic>R, T</italic>) gravity where the coupling between geometry and the trace of the energy-momentum tensor makes the matter sector an explicit part of the minisuperspace dynamics. The gravitational Hamiltonian, canonical momenta, and potential are derived, leading to the corresponding Schr&#246;dinger&#8211;Wheeler&#8211;DeWitt (SWDW) equation. The wave function of the universe is obtained for specific forms of <italic>f</italic>( <italic>R, T</italic>), and the results are compared with previous studies in <italic>f</italic>( <italic>R</italic>) and <italic>f</italic>( <italic>R, T</italic>) models, highlighting the role of matter-geometry coupling in the emergence of quantum cosmological dynamics.

Türkiye

Serkan Doruk Hazinedar

Yaghoub Heydarzade

Shahram Jalalzadeh

Quantum cosmology in <italic>f</italic>( <italic>R, T</italic>) theory with Schutz&#8217;s perfect fluid

We extract the non-perturbative heavy quark effective theory (HQET) parameters from the inclusive semi-leptonic decay $ \Lambda_c^+ \to X e^+ \nu_e $ . Unlike charmed mesons produced near the threshold, $ \Lambda_c^+ $ baryons produced in $ e^+e^- $ annihilation exhibit a complex momentum distribution, which makes the transformation of the electron energy spectrum from the laboratory frame to the $ \Lambda_c^+ $ rest-frame non-trivial. To address this issue, we develop a novel Bayesian inference method to reconstruct the electron energy moments in the $ \Lambda_c^+ $ rest-frame. We determine the HQET parameters $ \mu_\pi^2(\Lambda_c^+) $ and $ \rho_D^3(\Lambda_c^+) $ for the first time using a purely data-driven approach by performing a global fit of theoretical predictions in the 1S mass scheme to these extracted moments.

Dong Xiao

Kangkang Shao

Bayesian extraction of HQET parameters from the inclusive semi-leptonic decay of the $ {\Lambda_c^+} $ baryon * Supported in part by Natural Key R&D Program of China (2023YFA1609400) and National Natural Science Foundation of China (NSFC) (12105127)

The strong coupling $\textit{α}$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing its $\textit{u}$ = 1/2 renormalon and summing up the associated large (infrared) logarithms which, in combination with radius-dependent renormalization scales (called profile functions) extends the validity of perturbation theory to distances up to ~ 0.5 fm. Furthermore, we resum large ultrasoft logarithms to N LL accuracy using renormalization group evolution. We have checked that the standard four-loop R-evolution treats N LL and higher remnants in a non-symmetric way, hence we also account for this potential bias. Our estimate of the perturbative uncertainty is based on a random scan over the parameters specifying the profile functions and the treatment of R-evolution. We also devise a method to statistically combine into a single dataset results from independent simulations which use different lattice spacing and cover various ranges, which can be used to carry out fits in a much faster way. We explore the dependence of the extracted $\textit{α}$ value on the smallest and largest distances included in the dataset, on how R-evolution is treated, on how the fit is performed, and on the accuracy of ultrasoft resummation. From our final analysis, after evolving to the $\textit{Z}$-pole we obtain $$ {\alpha}_s^{\left({n}_f=5\right)}\left({m}_Z\right)=0.1170\pm 0.0009 $$ , compatible with the world average with the same incertitude.

Spain

Jose Mena-Valle

Vicent Mateu

Pablo Ortega

A precise $\textit{α}$ $\textit{s}$ determination from the R-improved QCD static energy