The deflection of light in the gravitational field of a massive body can be analyzed through diverse theoretical approaches. The null geodesic approach is commonly employed to calculate light deflection within strong and weak field limits. Alternatively, several studies have explored the gravitational deflection of light using the material medium approach. For a static, non-rotating spherical mass, the deflection in a Schwarzschild field can be determined by expressing the metric in an isotropic form and evaluating the refractive index to trace the light ray’s trajectory. In this study, we extend the above-mentioned approach to the Kerr–Sen black hole spacetime in heterotic string theory, a solution representing a rotating, charged solution in heterotic string theory. The frame-dragging effects inherent to the Kerr–Sen geometry are incorporated to compute the velocity of light rays, enabling the derivation of the refractive index in this field. Considering the far-field approximation, we calculate the deflection of light in the Kerr–Sen spacetime and compare our results with those obtained for the Kerr and Schwarzschild black hole solution in GR.

India

Saswati Roy

Shubham Kala

Atanu Singha

South Africa

Hemwati Nandan

Asoke Sen

Deflection of light due to Kerr Sen black hole in heterotic string theory using material medium approach

The Kerr-MOG black hole has recently attracted significant research attention and has been extensively applied in various fields. To accurately characterize the long-term dynamical evolution of charged particles around a Kerr-MOG black hole, it is essential to utilize numerical algorithms that are high-precision, stable, and capable of preserving the inherent physical structural properties. In this study, we employ explicit symplectic algorithms combined with the Hamiltonian splitting technique to numerically solve the equations of motion for charged particles. Initially, by decomposing the Hamiltonian into five integrable components, three distinct explicit symplectic algorithms ($\textit{S}$2, $\textit{S}$4, and $$PR{K_6}4)$$ are constructed. Numerical experiments reveal that the $$PR{K_6}4$$ algorithm achieves superior accuracy. Subsequently, we utilize Poincaré sections and the fast Lyapunov indicator (FLI) to investigate the dynamic evolution of the particle. Our numerical results demonstrate that the energy $\textit{E}$, angular momentum $\textit{L}$, magnetic field parameter $$\beta ,$$ black hole spin parameter $\textit{a}$, and MOG parameter $$\alpha $$ all significantly influence the particle’s motion. Specifically, the chaotic region expands with an increase in $\textit{E}$, $$\beta ,$$ or $$\alpha ,$$ but contracts with an increase in $\textit{a}$ or $\textit{L}$. Furthermore, when any two of these five parameters are varied simultaneously, it becomes evident that $\textit{a}$ and $\textit{L}$ predominantly dictate the system’s behavior. This study not only offers novel insights into the chaotic dynamics associated with Kerr-MOG black holes but also extends the application of symplectic algorithms in strong gravitational fields.

China

Zhenmeng Xu

Dazhu Ma

Wenfu Cao

Kai Li

Chaotic motion of charged test particles in a Kerr-MOG black hole with explicit symplectic algorithms

This study examines the validity of the Generalized Second Law of Thermodynamics (GSLT) to generalized Chaplygin gas (GCG) and modified Chaplygin gas (MCG) models within the general relativity(GR) framework and modified gravity framework namely the $\textit{f}$($\textit{T}$) gravity. Three distinct models of GCG and MCG are analyzed with bulk viscosity included in the GR framework to account for the dissipative process during cosmic evolution while the $\textit{f}$($\textit{T}$) gravity is considered without bulk viscosity. To study the thermodynamic implications of the model, our study employs three distinct forms of entropy: Tsallis, Barrow and Sharma–Mittal entropy. Furthermore, a highly generalized version of holographic cutoff has also been explored under the purview of the reconstruction approaches under consideration inspired by $\textit{The European Physical Journal C}$, 77:1–8. Our results confirm that the models satisfy the GSLT with total entropy change remaining positive thus confirming the thermodynamic stability of GCG and MCG and the robustness of these forms of entropy in describing the universe’s thermodynamic behaviour. Additionally, for the two Chaplygin gas models with bulk viscosity in the GR framework, the GSLT is validated and the results show the thermodynamical stability of these models with the inclusion of bulk viscosity term and interaction terms as well.

Khandro Chokyi

Surajit Chattopadhyay

Testing generalized second law of thermodynamics in cosmological models with bulk viscosity and modified gravity

This research work investigates the holographic dark energy cosmological model in the n-dimensional Kaluza–Klein space-time in the scalar–tensor theory of gravitation proposed by Brans–Dicke. A deterministic solution of the field equations is obtained and physical and kinematical properties of the obtained model are analysed through graphical representation. The density parameters of the dark matter and holographic dark energy are examined in detail. Also, the stability of cosmological model is ensured by using perturbation of metric. Furthermore, the diagnostic tools such as jerk parameter, statefinder pair, energy conditions and $$\omega _{\lambda } -{\omega }'_{\lambda }$$ plane are also studied to study the cosmological evolution.

S. Wankhade

A. Nimkar

Stability of n-dimensional Kaluza–Klein cosmological model in scalar–tensor theory of gravitation proposed by Brans–Dicke

This paper addresses a potential validation of the weak gravity conjecture (WGC) with the weak cosmic censorship conjecture (WCCC), as a significant challenge in quantum gravity. We explore the viability of the WGC and WCCC in the context of the Kerr-Newman-Kiselev-Letelier (KNKL) black hole. Although these conjectures appear unrelated, but surprising connection between these conjectures establishes a bridge between the quantum and the cosmic. By imposing specific constraints on the black hole's parameters, we demonstrate that the WGC and WCCC can be compatible in certain regions. We examine the properties of the KNKL black hole for <math altimg='si1.svg'><mi>q</mi><mo stretchy='false'>/</mo><mi>m</mi><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><msub><mrow><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>/</mo><mi>M</mi><mo stretchy='false'>)</mo></mrow><mrow><mi>e</mi><mi>x</mi><mi>t</mi></mrow></msub></math>, where <math altimg='si2.svg'><msub><mrow><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>/</mo><mi>M</mi><mo stretchy='false'>)</mo></mrow><mrow><mi>e</mi><mi>x</mi><mi>t</mi></mrow></msub></math> is the charge-to-mass ratio of a large extremal black hole. We present figures to test the validity of both conjectures simultaneously. Without the spin parameter <italic>a</italic>, the cloud of string parameter <italic>b</italic>, quintessence parameter <italic>&#947;</italic>, and equation of state parameter <italic>&#969;</italic>, the black hole either has two event horizons if <math altimg='si3.svg'><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&#8804;</mo><mn>1</mn></math> or none event horizon if <math altimg='si4.svg'><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mn>1</mn></math> which leads to a naked singularity that contradicts the WCCC. However, when <italic>a</italic>, <italic>b</italic>, <italic>&#947;</italic>, and <italic>&#969;</italic> are present, the black hole has event horizons in some regions in the <math altimg='si4.svg'><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mn>1</mn></math> that ensure the singularity is covered and both the WGC and WCCC are fulfilled. Actually, we face this issue in the extremality state of the black hole viz these conjectures remain viable, with the black hole maintaining an event horizon. We conclude that certain regions of <italic>a</italic>, <italic>b</italic>, <italic>&#947;</italic>, and <italic>&#969;</italic> parameters can make the WGC and WCCC compatible, indicating their agreement when these parameters are present.

Iran

Saeed Noori Gashti

Azerbaijan

Behnam Pourhassan

Cosmic-quantum connections: Assessing the viability of weak gravity and weak cosmic censorship conjectures in Kerr-Newman-Kiselev-Letelier black hole

J-PARC E05 reported recently a hint of a <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>11</mn></mrow></msup><mi mathvariant='normal'>B</mi></math> nuclear state in the <math altimg='si17.svg'><mmultiscripts><mrow><mi mathvariant='normal'>C</mi></mrow><mprescripts /><none /><mrow><mn>12</mn></mrow></mmultiscripts><msubsup><mrow><mo stretchy='false'>(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mo>,</mo><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mo stretchy='false'>)</mo></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>12</mn></mrow></msubsup><mrow><mi mathvariant='normal'>Be</mi></mrow></math> spectrum, bound by <math altimg='si3.svg'><msub><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>8.9</mn><mo>&#177;</mo><msubsup><mrow><mn>1.4</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>3.1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>3.8</mn></mrow></msubsup></math> MeV. Using a density-dependent &#926;-nuclear optical potential <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math> we explore to what extent a <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> assignment of this nuclear state is compatible with <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> and <math altimg='si6.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>p</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> nuclear-state interpretations of <math altimg='si7.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></math> capture events in light emulsion-nuclei experiments. We find that the only acceptable <math altimg='si5.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup></math> assignment at present, barring an abnormally strong repulsive <math altimg='si8.svg'><msup><mrow><mi>&#961;</mi></mrow><mrow><mn>2</mn></mrow></msup></math> component of <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math>, is that for the <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>11</mn></mrow></msup><mi mathvariant='normal'>B</mi></math> signal. This finding supports reassigning <math altimg='si7.svg'><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup></math> capture events in 14N, originally assigned as <math altimg='si9.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>s</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>14</mn></mrow></msup><mi mathvariant='normal'>N</mi></math> nuclear states, to <math altimg='si10.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mn>1</mn><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow><mrow><mn>14</mn></mrow></msup><mi mathvariant='normal'>C</mi></math> nuclear states. The depth of <math altimg='si24.svg'><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><mi>&#961;</mi><mo stretchy='false'>)</mo></math> at nuclear-matter density <math altimg='si11.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mn>0</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.17</mn></math> fm &#8722;3 is then <math altimg='si12.svg'><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><msubsup><mrow><mi>V</mi></mrow><mrow><mi mathvariant='normal'>opt</mi></mrow><mrow><mi mathvariant='normal'>&#926;</mi></mrow></msubsup><mo stretchy='false'>(</mo><msub><mrow><mi>&#961;</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy='false'>)</mo><mo>&#8776;</mo><mn>21</mn></math> MeV.

Israel

E. Friedman

A. Gal

Compatibility of recent Ξ-nuclear bound state signals

We investigate the <math altimg='si1.svg'><mi mathvariant='script'>N</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2</mn></math> supersymmetric generalization of the dual equivalence between the Maxwell-Chern-Simons model and two massive self-dual models. One of the self-dual models is described by a real scalar superfield, while the other is described by a chiral spinor superfield. The equivalence is analyzed in the presence of dynamical matter chiral superfields. Initially, we establish the duality by demonstrating the existence of master actions that interpolate between the models. We then show that the field equations are identical when the proper identifications are made. Finally, we confirm the dual equivalence by defining a master generating functional, which, after changing the variables, provides the generating functionals of the Maxwell-Chern-Simons model and the two massive self-dual models coupled to matter.

Brazil

F.S. Gama

J.R. Nascimento

A.Yu. Petrov

P. Porfirio

Dual equivalence between the Maxwell-Chern-Simons theory and two self-dual massive models interacting with matter in <math altimg='si1.svg'><mi mathvariant='script'>N</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2</mn></math>, <italic>d</italic>&#8239;=&#8239;3 superspace

Here we investigate a general class of massless local theories of spin 2 and spin 3, both invariant under generalized transverse diffeomorphisms (TDiff). We identify the ghost-free region in their parameter space and show the relationship of those models with the “doublet” action stemming from the tensionless limit of the open bosonic string field theory (for symmetric tensors). The connection is implemented via a nonlocal field redefinition which introduces a Stueckelberg-like field of rank 0 (rank 1) for the spin-2 (spin-3) case. An apparent mismatch between most TDiff models and the “doublet” action has led us to prove a nontrivial equivalence among TDiff models, thereby restoring consistency. Any point in the parameter subspace of ghost-free TDiff models is equivalent to any other one within that subspace. In particular, they are all physically equivalent to their simplest versions known as Maxwell-like models. So, the physical TDiff models seem to differ from each other by a Becchi-Rouet-Stora-Tyutin cohomologically trivial term.

R. Schimidt Bittencourt

D. Dalmazi

B. dos S. Martins

E.L. Mendonça

Equivalence of spin-2 and spin-3 models invariant under transverse diffeomorphisms and the tensionless limit of string theory

The inverse seesaw mechanism provides a concise scenario to produce tiny neutrino masses. Here we investigate the Majoron dark matter arising from the $$\mathrm{U(1)_L}$$ symmetry spontaneous breaking and matter–antimatter asymmetry in the framework of a high scale inverse seesaw mechanism. Due to the existence of a lepton-number-violating mass term, the Majoron gets its mass from radiative corrections. On the other hand, the Noether’s theorem indicates that the Majoron can obtain a non-zero initial velocity in the early universe, and then generates the relic abundance via kinetic misalignment mechanism. With the same initial Majoron velocity, the observed baryon asymmetry can also be explained through the so-called spontanous bayogenensis mechanism.

Ying-Quan Peng

Xiu-Fei Li

Cogenesis of Majoron dark matter and baryon asymmetry from a high scale inverse seesaw mechanism

The Hubble tension has profoundly shaped modern cosmological research. This study explores its impact on the early-universe physics in the modified emergent dark energy (MEDE) and $$\Lambda $$ CDM model using Planck PR4, BK18, DESI2024/2025, and supernova samples (Pan+, Union3). First, Hubble constant negligibly affects the tensor-to-scalar ratio ( $$r < 0.031$$ at 95%C.L.). Inclusion of DESI2025 achieves a 46% uncertainty reduction in key parameters. For CMB power spectra, DESI systematically amplifies TT/BB spectral discrepancies. Second, electron ionization fractions $$X_e(z)$$ display pronounced deviations from the $$\Lambda $$ CDM model at $$z=9.17$$ , suggesting a connection between Hubble tension and reionization history. This finding resonates with JWST measurements on high-redshift galaxy evolution. Future observations, such as 21-cm surveys, are highly anticipated to resolve these tensions by probing early-universe evolution and dark energy interactions.

Ming-Jian Zhang

Maoyou Yang

Junmei Wang

Testing influence of Hubble tension on the early Universe