We investigate the thermodynamic phase transitions of a four-dimensional charged anti-de Sitter black hole endowed with a non-minimal coupling of the form $$F^{\alpha \beta }F^{\gamma \lambda }R_{\alpha \gamma \beta \lambda }$$ . Using perturbative methods, we derive a consistent black hole solution and analyze its thermodynamics through both conventional equilibrium techniques and a topological defect classification approach. In the canonical ensemble, the system displays van der Waals-like critical behavior, with a swallow-tail structure in the free energy and distinct phase branches. In the grand canonical ensemble, by contrast, the system exhibits a Hawking–Page-like transition, characterized by a single divergence in the heat capacity and the absence of a swallowtail. The topological analysis independently confirms both types of critical behavior: it classifies the canonical ensemble within class $$W^{1+}$$ and the grand canonical ensemble within class $$W^{0-}$$ . Our results demonstrate that the non-minimal coupling preserves the universal topological classification while allowing ensemble choice to fundamentally alter the phase structure.

Iran

Mehdi Sadeghi

Faramaz Rahmani

Thermodynamic topology of 4D charged AdS black holes with $$F^{\alpha \beta }F^{\gamma \lambda }R_{\alpha \gamma \beta \lambda }$$ coupling

We analyse warping corrections to the scalar potential in flux compactifications of Type IIB string theory, focusing on their effect on $\textit{F}$-term de Sitter uplifting in Calabi-Yau orientifold models. A systematic inverse-volume expansion allows us to derive the four-dimensional off-shell potential in the presence of warping and non-ISD 3-form fluxes. This corresponds to integrating out all massive Kaluza-Klein modes using the ten-dimensional equations of motion. We further propose a warped Kähler potential in four-dimensional 𝒩 = 1 supergravity, and show that it is consistent with our ten-dimensional results. In the KKLT framework, we find that classical warping corrections, as well as mixed corrections involving non-ISD fluxes and quantum effects, are dominant, rendering the scenario effectively uncontrollable with current methods. By contrast, in LVS-like constructions these corrections are suppressed by inverse powers of the volume, specifically 𝒱 or 𝒱 , depending on the concrete model.

Germany

Arthur Hebecker

France

Severin Lüst

United States

Andreas Schachner

Simon Schreyer

Effective potentials, warping, and implications for $\textit{F}$-term uplifting

In this work, we investigate the structural and physical properties of anisotropic compact stars by incorporating the Einasto dark matter density profile within the <italic>f</italic>( <italic>R, T</italic>) gravity framework. The primary objective is to understand how the interplay between modified gravitational dynamics and dark matter influences the behavior of compact stellar systems. We construct physically viable stellar configurations by solving the modified field equations under appropriate boundary and matching conditions. The resulting models are analyzed using key physical criteria such as regularity, energy conditions, and stability requirements, including the behavior of the anisotropy factor and the adiabatic index. Our analysis, applied to five well-known compact star models, demonstrates that the proposed framework yields consistent and realistic solutions, offering deeper insights into the role of extended gravity theories and dark matter in astrophysical modeling.

India

H. Aruna Kumara

Chaitra Chooda Chalavadi

V. Venkatesha

Influence of the Einasto density profile on anisotropic compact stars in <italic>f</italic>( <italic>R, T</italic>) gravity

We study the cosmological dynamics of the quadratic symmetric teleparallel gravity model <math altimg='si8.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>&#945;</mi><msup><mi>Q</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi></mrow></math>, which introduces an <italic>H</italic> <sup>4</sup> correction to the Friedmann equation due to <italic>Q</italic>&#8733; <italic>H</italic> <sup>2</sup>. Using the exact algebraic solution for <italic>H</italic>( <italic>z</italic>), we reconstruct the effective dark-energy sector and compare the background evolution with &#923;CDM using Type Ia supernovae, BAO, and cosmic-chronometer data. At the perturbative level, the model modifies the Poisson equation through a time-dependent effective gravitational coupling <math altimg='si9.svg'><mrow><msub><mi>G</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>G</mi><msup><mrow><mo stretchy='true'>[</mo><mn>1</mn><mo>+</mo><mstyle scriptlevel='0' displaystyle='false'><mfrac><mn>2</mn><mn>3</mn></mfrac></mstyle><mi>A</mi><msup><mi>E</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo stretchy='true'>]</mo></mrow><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></mrow></math>, where <math altimg='si10.svg'><mrow><mi>A</mi><mo linebreak='goodbreak'>=</mo><mn>18</mn><mi>&#945;</mi><msubsup><mi>H</mi><mrow><mn>0</mn></mrow><mn>2</mn></msubsup></mrow></math>. For <italic>&#945;</italic>&#8239;&gt;&#8239;0 this produces a weakened gravitational interaction, suppressing the linear growth factor <italic>D</italic>( <italic>z</italic>), the growth rate <italic>f</italic>( <italic>z</italic>), and the RSD observable <italic>f&#963;</italic> <inf>8</inf>( <italic>z</italic>). In the nonlinear regime, the reduced gravitational strength increases the spherical-collapse threshold and suppresses the halo mass function, leading to a lower predicted value of <math altimg='si11.svg'><mrow><msub><mi>S</mi><mn>8</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#963;</mi><mn>8</mn></msub><msqrt><mrow><msub><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mi>m</mi></msub><mo linebreak='badbreak'>/</mo><mn>0.3</mn></mrow></msqrt></mrow></math>. Thus, the quadratic <italic>f</italic>( <italic>Q</italic>) extension can reproduce mild deviations from &#923;CDM at the background level while naturally alleviating the <italic>S</italic> <inf>8</inf> tension, offering a viable modified-gravity explanation for recent observational hints of dynamical dark energy.

Egypt

G.G.L. Nashed

Russia

P.V. Tretyakov

Saudi Arabia

A. Eid

Late-time cosmology and structure formation in quadratic <italic>f</italic>( <italic>Q</italic>) gravity

We initiate a systematic study on how to extract planar integrands of (supersymmetric) scattering amplitudes with $\textit{L}$ loops and $\textit{n}$ legs in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the recently proposed (bosonic) generating function for squared amplitudes with $\textit{N}$ := $\textit{n}$+$\textit{L}$ dual points; the latter enjoys a hidden permutation symmetry $\textit{S}$ and is given by a linear combination of weight-3 planar $\textit{f}$ -graphs that can be recast as bipartite graphs, which manifest important properties of ABJM amplitudes. We provide evidence that it contains sufficient information to reconstruct individual amplitudes, despite the absence of squared amplitudes at odd loops. The extraction of the four-point amplitude is already non-trivial and closely parallels the extraction of five-point amplitudes in $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM) from weight-4 $\textit{f}$-graphs: we comment on this similarity and provide new results for $\textit{n}$ = 4 ABJM loop integrand up to $\textit{L}$ = 6. For higher multiplicities, based on Yangian invariants (including BCFW building blocks for tree amplitudes) and an appropriate basis of planar dual conformal invariant(DCI) integrands, we disentangle six-point integrands up to two loops and eight-point tree amplitude from the squared amplitudes. Our results suggest that ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes, closely paralleling the role of $\textit{f}$-graphs in $$ \mathcal{N} $$ = 4 SYM.

China

Song He

United Kingdom

Yao-Qi Zhang

Loops and legs: ABJM amplitudes from $\textit{f}$-graphs

A modified gravitational model whose action is given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field, and its kinetic term is investigated as an extension of the gravitational sector including an additional dynamical degree of freedom. Within this framework, the causal structure of rotating cosmological solutions is analyzed by considering Gödel and Gödel-type spacetimes as background geometries used as theoretical probes of the model consistency. Different matter sources are examined, including a perfect fluid and scalar-field configurations. It is found that the standard Gödel metric is not compatible with the scalar sector of the theory unless the model reduces to the General Relativity limit. In contrast, Gödel-type geometries admit a wider class of solutions whose causal properties depend on the model parameters and on the matter content. In particular, perfect-fluid sources may lead to either causal or noncausal configurations, whereas scalar-field configurations constrain the geometry to the causal limit, preventing the formation of closed timelike curves, highlighting that the scalar field plays a nontrivial dynamical role distinct from that of a cosmological constant.

Brazil

L. Evangelista

M. Silva

J. Moretti

A. Santos

Causality and its violation in $$f(R,\mathcal {L}_m,\phi ,g^{\mu \nu }\nabla _\mu \phi \nabla _\nu \phi )$$ gravity

In this paper we consider the localization of the gravitino field on a codimension-one thick brane within the framework of $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) gravity. First, setting $$F(\phi ) = \phi $$ , we derive the potential functions for various parameters. Under appropriate coupling parameters, we can find the localized zero mode and some resonance states. Furthermore, we use these resonance states as initial data to investigate the evolution of the gravitino resonances. It can be observed that various parameters on the brane affect the evolution duration. We focus on comparing the localization behavior of the gravitino field on the brane for the cases with $$k=0$$ and $$k\ne 0$$ .

Xiang-Nan Zhou

Miao Wang

Zhi-Chao Duan

Localization of gravitino field on $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) brane

In this paper, we investigate static, spherically symmetric traversable wormholes in the framework of symmetric teleparallel <italic>f</italic>( <italic>Q, T</italic>) gravity by considering the linear model <math altimg='si5.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi><mi>T</mi></mrow></math>. By assuming a constant redshift function to describe zero tidal force geometries, we derive the corresponding field equations and obtain an analytic solution for the shape function by adopting a radially dependent equation of state of the form <math altimg='si6.svg'><mrow><msub><mi>p</mi><mi>r</mi></msub><mo linebreak='goodbreak'>+</mo><mi>&#969;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mi>&#961;</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, with <math altimg='si7.svg'><mrow><mi>&#969;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>A</mi><msup><mi>r</mi><mi>n</mi></msup></mrow></math>, where <italic>A</italic>&#8239;&gt;&#8239;0 and <italic>n</italic>&#8239;&gt;&#8239;0 are constants. The resulting wormhole configuration satisfies the fundamental geometric requirements, including the throat condition, the flare&#8211;out condition, and asymptotic flatness. The energy density remains positive and decreases with radius, while the null energy condition is violated only in the radial direction near the throat, indicating a localized exotic matter region. A Tolman&#8211;Oppenheimer&#8211;Volkoff analysis confirms that equilibrium is achieved through the balance between hydrostatic and anisotropic forces. Furthermore, the volume integral quantifier shows that the total amount of NEC&#8211;violating matter can be made arbitrarily small and confined close to the throat. The embedding diagrams support the geometric consistency of the solution. These results indicate that linear <italic>f</italic>( <italic>Q, T</italic>) gravity with a variable equation of state admits viable traversable wormhole solutions with minimized exotic matter content.

Morocco

Azerbaijan

M. Koussour

H.M. ElKhair

Uzbekistan

N. Kurbonov

J. Rayimbaev

M.K.M. Ali

Static traversable wormholes supported by a variable equation of state in <italic>f</italic>( <italic>Q, T</italic>) gravity

One of the most popular competitors to the CDM paradigm as an explanation for the late-time acceleration of the universe is the modification of general relativity (GR), with models such as <italic>f</italic>( <italic>R</italic>) gravity among the main motivations. In this study, we consider an exponential <italic>f</italic>( <italic>R</italic>) gravity model as a possible extensions of the GR. The extra scalar degrees of freedom and their effects on the cosmic expansion and structure formation are continuously considered in this scenario. By combining the PPS, BBN, CC, DESI-DR2, and CMB datasets, we imposed limitations on this model. We performed a detailed statistical analysis of the free model parameter <italic>b</italic> together with the standard cosmological parameters. Our analysis yields values of <italic>H</italic> <inf>0</inf> that are slightly lower than those obtained in &#923;CDM, indicating no significant relaxation of the <italic>H</italic> <inf>0</inf> tension. In contrast, the model predicts systematically higher values of <italic>S</italic> <inf>8</inf>, leading to a moderate alleviation of the <italic>S</italic> <inf>8</inf> tension by up to &#8239;&#8764;&#8239;1.2 <italic>&#963;</italic> when late-time datasets are included. Overall, these results demonstrate that although the considered <italic>f</italic>( <italic>R</italic>) gravity model does not resolve all cosmological tensions simultaneously, it provides a consistent improvement in the description of large-scale structure formation.

Saurabh Verma

Archana Dixit

Anirudh Pradhan

M.S. Barak

Testing exponential <italic>f</italic>( <italic>R</italic>) gravity with CMB, DESI-DR2, and supernova data

The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term while the boundary term do not contribute to the dynamics. The advantage of the proposition is that the stellar structure equations are up to order two, thus the theory is not haunted by ghosts. We obtain explicitly the defining equations for the thermodynamical variables and the geometry for the pure quadratic case, since the linear case amounts to general relativity. In trying to establish the vacuum geometry associated with the theory it turns out that two possible metrics emerge through the vanishing of the energy-momentum tensor. Next, we analyse the isotropy equation and make the observation that it is autonomous. It is rare that this happens in astrophysical modelling. This behaviour prompted the use of dynamical systems to understand the stability properties of fixed points or invariant submanifolds. It was necessary to choose a gauge in order to split the autonomous equation into a system from which we could plot a phase portrait and deduce the stability of solution trajectories. We find that the invariant submanifolds were generally stable with nearby paths approaching them.

South Africa

Sudan Hansraj

Christian Boehmer

Ndumiso Buthelezi

Dynamical systems approach to stellar modelling in $\textit{f}$($\textit{G}$, $\textit{B}$) gravity