Analyses of astrophysical observations, such as quasiperiodic oscillations (QPOs), combined with theoretical studies of particle oscillations, help understand black hole properties, determine black hole parameters, and test alternative gravity theories. In this study, we investigate the dynamics of charged particles orbiting magnetized black holes in a noncommutative (NC) geometry. We study the circular motion and oscillations of charged particles orbiting a black hole in the presence of a magnetic field, focusing on their applications to QPOs. First, we obtain solutions to the Maxwell equations for the orthonormal components of the magnetic field around black holes in the radial and angular directions, and analyze their dependence on the NC parameter and magnetic interactions. We analyze the effective potential, specific angular momentum, energy, and innermost stable circular orbits (ISCOs) of charged particles to demonstrate how the black hole spacetime, with magnetic interaction and NC parameters, affects particle dynamics. Then, we calculate the Keplerian, radial, and vertical epicyclic frequencies, providing insight into the orbital and oscillatory behavior of particles near the black hole. Furthermore, we investigate twin-peak QPOs using the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models and compare the main results with those of the standard Schwarzschild limit. Finally, we employ Monte Carlo Markov Chain (MCMC) simulations to obtain constraint values for black hole mass, the NC, and magnetic interaction parameters, using QPO frequency data observed in microquasars (XTE J1550-564, GRO J1655-40, GRS 1915+105), intermediate-mass (M82 X-1), and supermassive (SgrA*) BHs. Our findings may provide valuable insights into understanding the combined effects of NC spacetime and electromagnetic interactions around black holes on astrophysical observations of QPOs and on testing gravity theories in the strong-gravity regime.

Uzbekistan

Abubakir Shermatov

Czechia

Bekir Can Lütfüoğlu

Saudi Arabia

Ashfaque H. Bokhari

Pakistan

Azerbaijan

China

Faisal Javed

Javlon Rayimbaev

Sardor Murodov

Bahran Shermatov

Magnetized non-commutative inspired black holes: From charged particle dynamics to QPO studies

Distinguishing different subphases in the supercritical region is an important issue in statistical physics and condensed matter physics. Traditional approaches rely mainly on static thermodynamic response functions or equilibrium correlation functions, which are essentially limited to quasistatic processes. In this paper, we investigate the evolution behavior of a system after a rapid quench from the perspective of nonequilibrium dynamics within a holographic model. We find that, using the time at which inhomogeneous structures appear most rapidly, we can define a supercritical crossover curve based on the pure phase separation process. In addition, the uniform invasion phenomenon induced by topological defects persists in the supercritical region, and the invasion velocity exhibits a clear turning point as a function of the quench endpoint. This turning point can define another new nonequilibrium supercritical crossover line that simultaneously incorporates the effects of both symmetry breaking and phase separation. Unlike the classical Widom line or Frenkel line, these two new crossover lines contain both thermodynamic information and dynamical information, reflecting the dynamical nature of the supercritical region under nonequilibrium conditions. This work provides a novel nonequilibrium dynamical approach for characterizing supercritical subphases.

Zi-Qiang Zhao

Zhang-Yu Nie

Jing-Fei Zhang

Xin Zhang

Nonequilibrium crossover in the supercritical region from quench dynamics

Reconstructing the internal properties of hadrons in terms of fundamental quark and gluon degrees of freedom is a central goal in nuclear and particle physics. This effort lies at the core of major experimental programs, such as the Jefferson Lab 12 GeV program and the upcoming Electron-Ion Collider. A primary challenge is the inherent inverse problem: converting large-scale observational data from collision events into the fundamental quantum correlation functions (QCFs) that characterize the microscopic structure of hadronic systems within the theory of QCD. Recent advances in scientific computing and machine learning have opened new avenues for addressing this challenge using deep learning techniques. A particularly promising direction is the integration of theoretical calculations and experimental simulations into a unified framework capable of reconstructing QCFs directly from event-level information. In this work, we introduce a differential sampling method called the local orthogonal inverse transform sampling (LOITS) algorithm. We validate its performance through a closure test, demonstrating the accurate reconstruction of a test distribution from sampled events using Generative Adversarial Networks. The LOITS algorithm provides a central building block for addressing inverse problems involving QCFs and enables end-to-end inference pipelines within the framework of differential programming.

United States

Kevin Braga

Markus Diefenthaler

Steven Goldenberg

Daniel Lersch

Yaohang Li

Jian-Wei Qiu

Kishansingh Rajput

Felix Ringer

Nobuo Sato

Malachi Schram

Toward an event-level analysis of hadron structure using differential programming

Black hole thermodynamics has recently witnessed three distinct classification schemes: based on local geometric properties of the temperature function, global topological invariants, and Riemann surface foliations in the complex plane. We show that these schemes can be precisely mapped onto one another in the real domain via two dictionaries: one linking thermal stability to the monotonicity of the temperature curve, and the other connecting the number of black hole states to the foliation number of a Riemann surface. The number of extremal points of the temperature curve determines the classification in all three frameworks, tracing this unification to the critical point structure of the black hole solution space. As an illustration, several black holes demonstrate how counting extrema yields topological invariants and phase transition information. This unified framework simplifies black hole thermodynamic analysis and provides a foundation for exploring more complex black holes.

Shi-Hao Zhang

Shao-Wen Wei

Unifying topological, geometric, and complex classifications of black hole thermodynamics

First-order phase transitions of black holes have been extensively studied within thermodynamic frameworks, yet the corresponding evolution of spacetime geometric properties remains unclear. This paper establishes a purely differential geometric framework to probe such phase transitions by analyzing the curvature of unstable null orbits. Using the geodesic curvature of the null circular orbit in the optical metric to locate the light ring, we demonstrate that the corresponding Gaussian curvature <italic>K</italic> serves as a direct geometric signature of the phase transition. During a first-order phase transition, the curve <italic>K</italic> versus temperature <italic>T</italic> exhibits a multivalued structure within the spinodal region, precisely mirroring the swallowtail behavior of the free energy. Numerical analysis of Hayward-Letelier-AdS black holes confirms the effectiveness of this geometric signature. Our work demonstrates that the intrinsic geometric quantities of spacetime encode the information of black hole phase transitions. These quantities serve as geometric probes of black hole phase transitions, while their discontinuity between the small and large black hole branches exhibits order parameter-like behavior. As an extension of this geometric probe, we also find that the Gaussian curvature exhibits a heat&#8211;capacity&#8211;like divergence at the second&#8211;order phase transition point. These results provide a purely geometric foundation for understanding the correspondence between thermodynamics and spacetime curvature in the null case.

Zi-Yuan Li

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions

Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them. Poincaré-covariant equations of motion compatible with these rigidity conditions are proposed and discussed. The resulting theory has the expected six dynamical degrees of freedom, allowing for more general motions than in Born’s theory. Therefore, treating a relativistic body as a discrete system of particles could be a promising alternative to the standard approach based on Born’s rigidity conditions.

Brazil

Alexei A. Deriglazov

Dynamics of a relativistic discrete body: Rigidity conditions, and covariant equations of motion

In this work, we investigate the unquenched effects on the imaginary potential and thermal width within the framework of the AdS/CFT correspondence. Using the Nambu-Goto action, we find that the imaginary potential vanishes in the quenched system ( <math altimg='si2.svg'><mrow><msub><mi>N</mi><mi>f</mi></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>) due to confinement, while it becomes non-zero in the unquenched two-flavor ( <math altimg='si3.svg'><mrow><msub><mi>N</mi><mi>f</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math>) system, with its absolute value increasing monotonically as a function of the temperature-length parameter ( <italic>LT</italic>). The introduction of the flavors is found to significantly enhance the thermal width. Additionally, in the low-temperature regime, the inclusion of light quark flavors reduces the stopping distance. Furthermore, the onset of the imaginary potential occurs at earlier thresholds as the chemical potential increases.

Jing Zhou

Saiwen Zhang

Menjun Zhu

Effects of dynamical quark flavors on imaginary potential and thermal width in heavy quarkonium from AdS/CFT correspondence

We numerically study kink-antikink collisions in the self-gravitating <italic>&#981;</italic> <sup>4</sup> model coupled to the two-dimensional dilaton gravity theory proposed by Mann et al. The static kink solutions interpolate between an anti-de Sitter (AdS <inf>2</inf>) region and a Minkowski region, and can be regarded as two-dimensional analogues of certain thick branes. By scanning the initial velocity for several gravitational couplings, we find that gravity modifies the scattering structure: the resonance windows shift toward higher initial velocities and become progressively narrower as the coupling <italic>&#954;</italic> increases, while the critical escape velocity increases mildly. A linear perturbation analysis further indicates that the shape modes turn into long-lived quasi-bound states in the weak-gravity regime, which could leak energy during collisions and may therefore contribute to the shift and narrowing of the windows and the increase of the critical velocity. The collisions further produce a clear geometrical response: the conformal factor decreases after the collision, corresponding to a contraction of the local proper spatial scale in the conformal gauge, and this effect becomes stronger for larger <italic>&#954;</italic>. Meanwhile, the Ricci scalar develops transient peaks during kink encounters but remains finite in all simulations considered. Thus, in contrast to higher-dimensional thick-brane collisions, we find no evidence for spacetime singularity formation in this two-dimensional model.

Zhen-Tao He

Yuan Zhong

Kink collisions in a two-dimensional gravity model

The Gerasimov–Drell–Hearn sum rule is a generic relation that has been used to make significant contributions to research in hadronic physics. It connects the spin-dependent cross-section for photoproduction off a particle to the squared ratio of the particle’s anomalous magnetic moment and its mass, ( <italic>&#954;</italic>/ <italic>M</italic>) <sup>2</sup>. Thus, for a nucleon embedded in a nucleus, the sum rule relates the cross-section to <italic>&#954;</italic>/ <italic>M</italic> averaged quadratically over the nucleons comprising the nucleus. This quadratic averaging can be used to constrain the mechanism responsible for the medium modification of the nucleon. We also point out that the global properties of the embedded nucleon like its axial charge, mass or magnetic moment are observables measurable through sum rules.

A. Deur

M.M. Dalton

Slovenia

S. Širca

Studying nuclear medium modification using the Gerasimov-Drell-Hearn sum rule

We propose a novel search strategy for the origin of neutrino mass at the High-Luminosity LHC (HL-LHC) exploiting the 4D spacetime structure of delayed displaced vertices. In the two-inert-doublet scotogenic model (2IDM3N), the heavy neutral fermion <italic>N</italic> <inf>2</inf> is a naturally long-lived particle (LLP) whose proper decay length <math altimg='si20.svg'><mrow><mi>c</mi><msub><mi>&#964;</mi><msub><mi>N</mi><mn>2</mn></msub></msub><mo>&#8764;</mo><mn>10</mn></mrow></math>&#8211;3000&#8201;mm is directly linked to the smallness of neutrino masses via the one-loop Yukawa coupling <math altimg='si21.svg'><mrow><mi>y</mi><mo>&#8764;</mo><mi mathvariant='script'>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></math>. Electroweak pair production of the inert scalars (e.g. <math altimg='si22.svg'><mrow><mi>p</mi><mi>p</mi><mo>&#8594;</mo><msup><mover accent='true'><mi>&#951;</mi><mo>&#732;</mo></mover><mo>&#177;</mo></msup><msup><mover accent='true'><mi>&#951;</mi><mo>&#732;</mo></mover><mn>0</mn></msup></mrow></math>, <math altimg='si23.svg'><mrow><msup><mover accent='true'><mi>&#951;</mi><mo>&#732;</mo></mover><mo>+</mo></msup><msup><mover accent='true'><mi>&#951;</mi><mo>&#732;</mo></mover><mo>&#8722;</mo></msup></mrow></math>) provides at least one hard prompt lepton for single-lepton triggering, while the subsequent decay <math altimg='si24.svg'><mrow><msub><mi>N</mi><mn>2</mn></msub><mo>&#8594;</mo><msub><mi>N</mi><mn>1</mn></msub><mo linebreak='goodbreak'>+</mo><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> produces a displaced vertex with a pair of leptons carrying a large time-of-flight delay &#916; <italic>t</italic>&#8239;&#8764;&#8239;300&#8201;ps relative to prompt particles. We demonstrate that a single cut &#916; <italic>t</italic>&#8239;&gt;&#8239;200&#8201;ps on the arrival time at the CMS MIP Timing Detector eliminates the dominant material-conversion background ( <math altimg='si6.svg'><mrow><mi>&#947;</mi><mo>&#8594;</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math>), rendering the search effectively background-free within the idealized detector simulation employed here. Full detector-level simulation at the benchmark point <math altimg='si2.svg'><mrow><msub><mi>m</mi><msub><mi>N</mi><mn>2</mn></msub></msub><mo linebreak='goodbreak'>=</mo><mn>150</mn><mspace width='0.16em' /><mtext>GeV</mtext></mrow></math>, <math altimg='si18.svg'><mrow><msub><mi>m</mi><msub><mi>N</mi><mn>1</mn></msub></msub><mo linebreak='goodbreak'>=</mo><mn>100</mn><mspace width='0.16em' /><mtext>GeV</mtext></mrow></math>, <math altimg='si3.svg'><mrow><mi>c</mi><msub><mi>&#964;</mi><msub><mi>N</mi><mn>2</mn></msub></msub><mo linebreak='goodbreak'>=</mo><mn>189</mn><mspace width='0.16em' /><mtext>mm</mtext></mrow></math> yields a signal efficiency of <math altimg='si25.svg'><mrow><mrow><mi>&#949;</mi></mrow><mo linebreak='goodbreak'>=</mo><mn>3.46</mn><mo>%</mo></mrow></math> and an expected yield of &#8239;&#8764;&#8239;10&#8201;800 signal events at <math altimg='si9.svg'><mrow><mn>3000</mn><mspace width='0.16em' /><msup><mtext>fb</mtext><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></mrow></math>, with negligible expected background (&#8239;&#8818;&#8239;1 event) based on analytic timing arguments and simplified detector modelling. The HL-LHC sensitivity covers the scotogenic parameter space corresponding to <math altimg='si26.svg'><mrow><mn>10</mn><mspace width='0.16em' /><mtext>mm</mtext><mo>&#8818;</mo><mi>c</mi><msub><mi>&#964;</mi><msub><mi>N</mi><mn>2</mn></msub></msub><mo>&#8818;</mo><mn>3000</mn><mspace width='0.16em' /><mtext>mm</mtext></mrow></math> for <math altimg='si27.svg'><mrow><mn>120</mn><mspace width='0.16em' /><mtext>GeV</mtext><mo>&#8818;</mo><msub><mi>m</mi><msub><mi>N</mi><mn>2</mn></msub></msub><mo>&#8818;</mo><mn>300</mn><mspace width='0.16em' /><mtext>GeV</mtext></mrow></math>.

Renjie Wang

Delayed displaced vertices at the HL-LHC: A novel window into the scotogenic mechanism