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

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

India

Faizuddin Ahmed

Türkiye

İzzet Sakallı

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

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 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

We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter’s groups and the associated word problem, we turn to the Artin presentation of the braid group and its quotients. We present various representations of the braid group as deterministic or non-deterministic finite state automata and discuss connections with <italic>q</italic>-Dicke states, as well as Lusztig and crystal bases. We propose the study of the eigenvalue problem of the <math altimg='si21.svg'><mrow><msub><mi mathvariant='fraktur'>U</mi><mi>q</mi></msub><mrow><mo>(</mo><msub><mi mathvariant='fraktur'>gl</mi><mi>n</mi></msub><mo>)</mo></mrow></mrow></math> invariant spin-chain like &#8220;Hamiltonian&#8221; as a systematic means for constructing canonical bases for irreducible representations of <math altimg='si22.svg'><mrow><msub><mi mathvariant='fraktur'>U</mi><mi>q</mi></msub><mrow><mo>(</mo><msub><mi mathvariant='fraktur'>gl</mi><mi>n</mi></msub><mo>)</mo></mrow><mo>.</mo></mrow></math> This is explicitly proven for the algebra <math altimg='si23.svg'><mrow><msub><mi mathvariant='fraktur'>U</mi><mi>q</mi></msub><mrow><mo>(</mo><msub><mi mathvariant='fraktur'>gl</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>.</mo></mrow></math> Special braid representations associated with self-distributive structures are also studied as finite automata. These finite state automata organize clusters of eigenstates of these braid representations.

United Kingdom

Anastasia Doikou

Braided finite automata and representation theory

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

Zitterbewegung (ZBW), arising from the interference between positive- and negative-energy solutions of the Dirac equation, is a characteristic feature of relativistic single-particle dynamics, but its explicit manifestation depends on the choice of position operator. We formulate relativistic vortex electron wave packets as coherent superpositions of Dirac plane-wave states and derive their exact spacetime evolution. For the canonical Dirac position, we show that orbital angular momentum substantially enhances and spatially structures the relative-coordinate contribution conventionally associated with ZBW. We then analyze the operator dependence of this result by separating the canonical position into a Foldy–Wouthuysen/Newton–Wigner (FW/NW) mean position and an oscillatory relative coordinate. For the vortex packets considered here, the FW/NW mean position exhibits only the ordinary centroid drift and no transverse trembling. However, the same vortex-enhanced radial scale survives in the positive-energy sector as a Berry-type geometric dressing of the projected position operator. The present work therefore identifies not a representation-independent trembling of the one-particle centroid, but a vortex-amplified remnant of Dirac interband mixing in an operationally meaningful position observable.

Zhongze Guo

Bei Xu

Qiang Gu

Vortex-enhanced Zitterbewegung in relativistic Dirac wave packets

Gravitational observables for binary systems exhibit a simple polynomial dependence on the masses <italic>m</italic> <inf>1</inf>, <italic>m</italic> <inf>2</inf> of the two scattering objects when they are written in terms of the appropriate kinematic variables in the post-Minkowskian (PM) regime. We point out that this property, combined with particle interchange symmetry, allows one to reconstruct the leading and <italic>subleading</italic> PM waveforms from their probe limit, <italic>m</italic> <inf>1</inf>&#8239;&#8811;&#8239; <italic>m</italic> <inf>2</inf>. As an application, focusing on their re-expansion in the small-velocity or post-Newtonian (PN) regime, we calculate the probe-limit waveforms up to 10PN, and then exploit this observation to deduce from them the waveforms for generic masses in the center-of-mass frame up to 5PN. To this end, we employ both the amplitude-based waveform integrands and the tail formula. This combined approach simplifies substantially the PN expansion of the full subleading PM waveform.

France

Carlo Heissenberg

Rodolfo Russo

Reconstructing the gravitational waveform from its probe limit

Using the convergent Leaver method, we investigate the quasinormal modes of a massive scalar field propagating in the background of the Casadio–Fabbri–Mazzacurati (CFM) brane-world black hole. We show that the spectrum exhibits two distinct types of modes, depending on their behavior as the field mass increases. In one class, the real oscillation frequency decreases and eventually approaches zero, while in the other the damping rate tends to vanish. When either the real or imaginary part of the frequency reaches zero, the corresponding mode disappears from the spectrum, and the first overtone replaces it. The emergence of modes with a vanishing real part at certain critical values of the field mass is a distinctive feature of the CFM spectrum.

Czechia

Bekir Can Lütfüoğlu

Uzbekistan

Sardor Murodov

Mardon Abdullaev

Javlon Rayimbaev

Munisbek Akhmedov

Muhammad Matyoqubov

Two types of quasinormal modes of Casadio-Fabbri-Mazzacurati brane-world black holes