By studying new decelerating sudden future singularity (SFS) universe, we report finding a novel type of cosmological singularity which we dub a finite time pseudo-rip (FTPR). In contrast to the new SFS model, where the expansion is decelerating before reaching the pressure singularity, the FTPR scenario is preceded by a super-accelerated phantom phase. Our claim is based on the thorough study of the energy conditions showing the violations of all of them for a FTPR, and only the dominant energy one for an SFS. Application of the so-called Raychaudhuri averaging shows that, alike within the requirement of geodesic completeness, these singularities are weak in the sense of this definition. We study the properties of the models including the behaviour of the cosmological horizons presented in the appropriate Penrose diagrams. Finally, we introduce a FTPR model containing standard radiation and dust fluids that can mimic the past expansion history of ΛCDM though facing a future pressure singularity.

Poland

Mariusz P. Da̧browski

Spain

Teodor Borislavov Vasilev

Finite time pseudo-rip singularity in cosmology

We have derived a rigorous theoretical proof of the Strutinsky energy theorem. This proof not only provides a proper interpretation of the shell-correction decomposition, resolving decades of confusion, but also lays a foundation for constructing nuclear density functionals.

Sweden

Chong Qi

Rigorous proof of the Strutinsky energy theorem and foundations of nuclear density functional theory

We develop an entropy-based formulation of gravitational focusing in Lorentzian geometry by associating a scalar entropy functional to timelike geodesic congruences. Rewriting the Raychaudhuri equation as an entropy production law, we show that entropy accumulation governs the evolution of the expansion scalar and drives finite-time focusing. We prove that when the integrated entropy exceeds a critical threshold set by the initial expansion, geodesic incompleteness necessarily follows. This result provides a quantitative refinement of the classical singularity theorems, replacing qualitative geometric conditions with an explicit entropy criterion. Our approach offers a thermodynamic interpretation of gravitational collapse and suggests that singularities arise as endpoints of irreversible entropy growth in spacetime.

India

Rohit Dhormare

An entropy-based criterion for geodesic incompleteness

Using Kolmogorov-Arnold Networks (KANs), we construct a holographic model informed by lattice QCD data. This neural network approach enables the derivation of an analytical solution for the deformation factor <italic>w</italic>( <italic>r</italic>) and the determination of a constant <italic>g</italic> related to the string tension. Within the KANs-based holographic framework, we further analyze heavy quark potentials under finite temperature and chemical potential conditions. Additionally, we calculate the drag force, jet quenching parameter, and diffusion coefficient of heavy quarks in this paper. Our findings demonstrate qualitative consistency with both experimental measurements and established phenomenological model.

China

Wen-Chao Dai

Ou-Yang Luo

Bing Chen

Italy

Xun Chen

Xiao-Yan Zhu

Xiao-Hua Li

Extracting transport properties from the heavy-quark potential with neural networks in a holographic model

The Kerr-Schild gauge is generalized to the case that the vector generating the deformation is not null. Contrary to naive expectations, this vector generates a finite expansion for the curvature tensor. We prove a theorem on the conditions for the deformed metric being Ricci flat, namely that the deformation vector must be irrotational (then geodesic) in the background spacetime.

Enrique Álvarez

Jesús Anero

Generalized Kerr-Schild gauge

We report a mass rule of Koide type with inverse shape, <display><formula id='ueq0001'><math altimg='si1.svg'><mrow><msub><mi>m</mi><mi>i</mi></msub><mo linebreak='goodbreak'>=</mo><msup><mi>M</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></msup><msup><mrow><mo>(</mo><msub><mi>w</mi><mn>0</mn></msub><mo>+</mo><msub><mi>w</mi><mi>i</mi></msub><mo>)</mo></mrow><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup><mo>.</mo></mrow></math></formula></display>It applies to the down-quark sector with numerical precision comparable to that of the direct charged-lepton sum rule <math altimg='si2.svg'><mrow><msub><mi>m</mi><mi>i</mi></msub><mo linebreak='goodbreak'>=</mo><msup><mi>M</mi><mrow><mo>(</mo><mi>l</mi><mo>)</mo></mrow></msup><msup><mrow><mo>(</mo><msub><mi>z</mi><mn>0</mn></msub><mo>+</mo><msub><mi>z</mi><mi>i</mi></msub><mo>)</mo></mrow><mn>2</mn></msup></mrow></math>. For central mass values, Koide ratio reaches exactly 2/3 near <italic>Q</italic>&#8239;&#8771;&#8239;280&#8201;TeV under Standard Model renormalisation-group running. We also review other rules of the direct kind involving quarks.

Alejandro Rivero

New sum rules of the Koide type

The process-independence of the color dipole amplitude is a cornerstone of high-energy Quantum Chromodynamics (QCD). However, standard phenomenological approaches typically rely on rigid parametric ansatzes and often require ad-hoc geometric adjustments to reconcile inclusive and diffractive measurements. To resolve this tension, we introduce Physics-Informed Neural Networks (PINNs) employing a “Teacher–Student” strategy. The physics-based momentum-space Balitsky-Kovchegov evolution dynamics act as the “Teacher,” constraining the solution manifold, while the network “Student” is refined against inclusive HERA <italic>F</italic> <inf>2</inf> data. This approach extracts a model-independent dipole amplitude without assuming initial states. Strikingly, we demonstrate that this amplitude&#8212;without parameter retuning or geometric rescaling&#8212;successfully predicts the absolute normalization and kinematic dependence of exclusive <italic>J</italic>/ <italic>&#968;</italic> photoproduction cross-sections. This parameter-free prediction of the saturation dynamics provides promising evidence for the process-independence of the gluon saturation scale and establishes PINNs as a transformative paradigm for uncovering non-perturbative QCD structures.

Wei Kou

Xurong Chen

Extraction of the color dipole amplitude with physics-informed neural networks

The ALICE and CMS Collaborations have analyzed a number of cumulants mixing elliptic flow ( <italic>v</italic> <inf>2</inf>) and triangular flow ( <italic>v</italic> <inf>3</inf>), involving up to 8 particles, in Pb+Pb collisions at the LHC. We unravel an unexpected simplicity in these complex mathematical quantities for collisions at fixed impact parameter. We show that as one increases the order in <italic>v</italic> <inf>2</inf>, for a given order in <italic>v</italic> <inf>3</inf>, the changes in the cumulants are solely determined by the mean elliptic flow in the reaction plane, which originates from the almond-shaped geometry of the overlap area between the colliding nuclei. We derive simple analytic relations between cumulants of different orders on this basis. These relations are in good agreement with recent data from the CMS Collaboration. We argue that agreement will be further improved if the analysis is repeated with a finer centrality binning. We make quantitative predictions for cumulants of order 10 which have not yet been analyzed.

Saudi Arabia

Mubarak Alqahtani

France

Jean-Yves Ollitrault

Explaining higher-order correlations between elliptic and triangular flow

In this paper, we obtain a charged Yukawa black hole solution in scalar-vector-tensor gravity (STVG), known as modified gravity (MOG). The aim of this study is to explore how the presence of the STV field modification and an additional Yukawa field impact particle dynamics, energy extraction, particle collisions, and radiation. After deriving the solution for a charged black hole surrounded by a Yukawa field, we analyze the motion of charged test particles in the equatorial plane, the effective potential, specific energy, and angular momentum as functions of the Yukawa parameters and particle charge, including the location of the innermost stable circular orbits (ISCOs). Our results indicate that the Yukawa coupling strength and the MOG field shift the ISCO outward. We also study the electric Penrose process involving charged particles near the black hole horizon. It is found that the inclusion of the Yukawa field enhances the process efficiency. Collisions of charged particles near the horizon are also studied by calculating the center-of-mass energy, which shows that the presence of the Yukawa coupling significantly amplifies the collision energy. Finally, the radiation luminosity of charged particles orbiting black holes via Bremsstrahlung is investigated and compared with the Reissner-Nordström case. This comparison suggests that Yukawa-field modifications leave observable imprints on orbital dynamics, energy extraction, and radiation, enabling the testing of modified gravity via astrophysical measurements.

Uzbekistan

Nuriddin Kurbonov

Javlon Rayimbaev

Ashfaque H. Bokhari

Bobomurat Ahmedov

Muhammad Zahid

Aleksandra Demyanova

Charged Yukawa-modified black holes: Electric Penrose, Bremsstrahlung radiation and collisions of charged particles

In this work, a systematic way of analysing the N Higgs Doublet Model flavour sector will be developed. We introduce a complete set of mixing matrices describing the rotation between certain suitably defined bases, akin to the Cabibbo-Kobayashi-Maskawa matrix, which describes the relation between the up-quark and down-quark mass bases. We point out the crucial importance played by the charged Higgs basis. A complete set of weak basis transformation invariant traces of flavour matrices for the general N doublets case is also introduced for the first time. This will be important for studies of the renormalization group evolution in terms of relevant physical parameters.

Portugal

João C. Belas

João P. Silva

Flavour invariants of the N Higgs doublet model