<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Electromagnetic modes are found for a brane orthogonal to AdS boundary.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Brane-induced contributions are extracted from two-point functions.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Brane-induced VEVs have opposite signs for PMC and PEC boundary conditions.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>Vacuum energy-momentum tensor has an off-diagonal describing shear force.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>Brane-induced vacuum energy density is positive for PMC condition.</para></list-item></list>

Armenia

A.A. Saharian

R.M. Avagyan

V.F. Manukyan

Electromagnetic Wightman functions and vacuum densities for a brane intersecting the AdS boundary

We present a new set of spacetime solutions for spiral galaxies corresponding to flat rotation curves at large distances. These correspond to anisotropic pressure, which could be sourced by either matter or geometry. As examples, we elucidate the galactic metrics corresponding to the non-ideal generalizations of ‘dust’ and ‘radiation’, respectively. Further, we find a dynamical realization of the Einstein cluster when the spatially averaged equation of state ( <italic>w</italic>) happens to be non-zero but small. The correction to the Einsteinian bending angle for a light ray penetrating a large galactic halo is predicted to be: <math altimg='si1.svg'><mrow><mo stretchy='true'>(</mo><mfrac><mrow><mn>2</mn><mo>+</mo><mn>3</mn><mi>w</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi>w</mi></mrow></mfrac><mo stretchy='true'>)</mo><mfrac><mrow><mi>&#960;</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><msup><mi>c</mi><mn>2</mn></msup></mfrac></mrow></math>, <italic>v</italic> being the limiting rotational velocity. We infer a mild decline <math altimg='si2.svg'><mrow><mo>(</mo><msup><mi>v</mi><mo>&#8242;</mo></msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo>&#8764;</mo><mo>&#8722;</mo><mfrac><mn>1</mn><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>)</mo></mrow></math> of the rotation curves at large radii for sufficiently luminous galaxies, as also indicated by some specific observations.

India

Sandipan Sengupta

Exact solutions with asymptotically flat galactic rotation curves

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>A BRST-quantized version of the 4D combined field-theoretic system of the Abeian 3-form and 1-form gauge theories is considered.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Nilpotent continuous (anti-)BRST and (anti-)co-BRST symmetry and discrete duality symmetry transformation operators are discussed.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>A unique continuous bosonic symmetry operator is constructed out of the above four nilpotent continuous symmetry operators.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>Importance of all the four Curci-Ferrari type restrictions has been highlighted in the proof of the uniqueness property.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>Algebraic structures of the discrete and continuous symmetry operators are obtained.</para></list-item></list>

R.P. Malik

A unique bosonic symmetry in a 4D field-theoretic system

We employ the island formula to investigate the entanglement entropy of the Hawking radiation in an asymptotically AdS black hole background within the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity. Through an analysis based on the Euclidean action, we find that the area term of the generalized entropy must be modified, which in turn leads to a modification of the island formula. Using the modified formula to compute the radiation entropy for an eternal asymptotically AdS black hole reveals that, the result diverges as the cutoff surface is moved outward, indicating the breakdown of the <italic>s</italic>-wave approximation. A possible reason is that we have neglected the gravitational back-reaction. For a collapsing asymptotically AdS black hole, the radiation entropy is dominated by the area term, with a correction proportional to the logarithm of the event horizon area, which is consistent with the predictions of quantum gravity. Both the radiation entropy and the Page time are ultimately influenced by the choice of the <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> model, implying that the information regarding the underlying gravitational model is encoded in the final radiation.

China

Yipeng Liu

Wei Xu

Baocheng Zhang

Radiation entropy in asymptotically AdS black holes within <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity

In this paper, we explicitly obtain the nonrelativistic Breit potential in the bumblebee model arising in the weak gravity limit of the metric-affine bumblebee gravity, coupled to the spinor matter. In this theory, in the lower (second) order in the small coupling constant <italic>&#958;</italic> (and the second order in the Lorentz-violating (LV) vector <italic>&#946;<inf>&#956;</inf></italic>) it demonstrates the 1/ <italic>r</italic> asymptotics, which naturally corresponds to the massless character of the theory, while higher orders in <italic>&#958;</italic> yield anisotropic modifications of the Coulomb potential due to the Lorentz symmetry breaking. For the lower-order modification of the effective potential, we calculate LV corrections to energy levels of the hydrogen atom.

Brazil

C. Furtado

J.R. Nascimento

A. Yu. Petrov

P. Porfirio

Nonrelativistic effective potential of the bumblebee model

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.

Pakistan

Hira Shadab

Azerbaijan

M. Sharif

Tayyab Naseer

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

We study the extended phase space thermodynamics of a charged Bardeen-Anti-de Sitter (AdS) black hole (BH) surrounded by perfect fluid dark matter (PFDM) and a cloud of strings (CS). The metric function carries five parameters: magnetic charge <italic>q</italic>, electric charge <italic>Q</italic>, CS parameter <italic>a</italic>, PFDM parameter <italic>&#946;</italic>, and cosmological constant &#923;. The CS enlarges the event horizon while PFDM reduces it. The entropy is fixed by the Bekenstein-Hawking area law <math altimg='si27.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mi>A</mi><mo linebreak='goodbreak'>/</mo><mn>4</mn></mrow></math>, in agreement with Wald&#8217;s Noether-charge prescription, and the thermodynamic analysis is carried out within the reduced thermodynamic phase space (RTPS) framework of Ma&#8211;Li&#8211;Shi and Ma&#8211;He&#8211;Wang&#8211;Li, in which all physical quantities are first defined in the full phase space of the underlying singular &#8220;mother&#8221; BH and are then projected onto the regular sector via the Bardeen regularity constraint. Thermal fluctuations yield positive corrections (&#916; <italic>S</italic>&#8239;&gt;&#8239;0) with relative magnitude below 18% for large BHs. The Joule-Thomson analysis shows that the Bardeen core and CS decrease the inversion temperature, contracting the cooling region. The critical ratio <math altimg='si28.svg'><mrow><msub><mi>&#961;</mi><mi>c</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>P</mi><mi>c</mi></msub><msub><mi>r</mi><mi>c</mi></msub><mo linebreak='goodbreak'>/</mo><msub><mi>T</mi><mi>c</mi></msub><mo>&#8776;</mo><mn>0.19</mn></mrow></math> deviates from the Reissner-Nordstr&#246;m-AdS universal value 3/8, while van der Waals-like phase transitions persist with mean-field exponents. For a rectangular heat engine cycle, the efficiency reaches 67% of the Carnot bound. Within the parameter window we sample, these results identify quantitative thermodynamic shifts produced by exotic matter fields surrounding regular AdS BHs, with the inherited and the new pieces separated explicitly in the body of the text.

Jordan

Ahmad Al-Badawi

Faizuddin Ahmed

Türkiye

İzzet Sakallı

Thermodynamics of charged Bardeen-AdS black hole with perfect fluid dark matter and cloud of strings

We investigate chaotic dynamics of classical strings propagating in the spacetime of charged Einstein–Euler–Heisenberg black holes. The analysis is based on Lyapunov indicators and explores how string energy, angular momentum, non-linear electromagnetic corrections, and global spacetime geometry shape the resulting dynamics. The motion naturally separates into inner and outer regimes, with chaotic behavior confined by geometric features of the background. Both asymptotically flat and anti–de Sitter configurations are considered. When the cosmological constant vanishes, inner trajectories become increasingly unstable as energy and angular momentum increase, while outer trajectories remain mostly regular except at high-energy scales. In contrast, the presence of a negative cosmological constant leads to chaos that is strongly localized near the event horizon. In this regime, instability of inner modes is highly sensitive to energy and is further strengthened by non-linear electromagnetic effects, whereas outer modes show limited deviation from regular motion. These results indicate that spacetime curvature and non-linear electrodynamics jointly control both the strength and spatial distribution of chaotic string motion near charged black holes. The findings may offer qualitative insight into irregular behavior expected in strong-gravity environments.

Anum Fayyaz

G. Abbas

M.R. Shahzad

Saudi Arabia

Tahani Mohammed Alrosaa

Walid Abdelfattah

Chaotic dynamics of string around a charged Einstein–Euler–Heisenberg–AdS black hole with a non-linear electromagnetic field

We investigate the multiparameter quantum estimation and quantum thermodynamics properties of a gravitational cat state (gravcat) system composed of two interacting massive particles confined in double-well potentials. The system is described by an effective Hamiltonian involving the energy splitting parameter <italic>&#969;</italic> and the gravitational coupling strength <italic>&#947;</italic>, while the interaction with a thermal environment is modeled through a Gibbs thermal state. Within the framework of quantum parameter estimation theory, we employ the quantum Fisher information matrix (QFIM) to analyze the precision limits for estimating the three fundamental parameters of the model, namely the gravitational coupling <italic>&#947;</italic>, the energy splitting <italic>&#969;</italic>, and the temperature <italic>T</italic>. Utilizing the symmetric logarithmic derivative (SLD) formalism within the QFIM framework, we derive the analytical expressions of the estimation bounds and evaluate the corresponding minimal variances associated with the quantum Cram&#233;r-Rao bound (QCRB). Both simultaneous and individual estimation strategies are investigated, and their performances are compared in different parameter regimes. Our results reveal the existence of optimal estimation regions where the precision is significantly enhanced and show that the relative efficiency of the estimation schemes strongly depends on the interaction strength, the energy gap, and the thermal environment. In addition, the thermodynamic behavior of the system is analyzed within the framework of a quantum Stirling cycle. The internal energy, entropy, heat exchanges, and work production are examined, allowing us to evaluate the efficiency of the gravcat-based quantum heat engine. The obtained results highlight the interplay between quantum metrology and quantum thermodynamics and demonstrate that the estimation of optimal parameter regimes can play an important role in optimizing the thermodynamic performance of gravitationally interacting quantum systems.

Morocco

Omar Bachain

Mohamed Amazioug

Rachid Ahl Laamara

Multiparameter quantum estimation and stirling engine performance in a gravitational cat state system

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.

Serkan Doruk Hazinedar

Yaghoub Heydarzade

Shahram Jalalzadeh

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