We investigate Josephson phenomena in a slowly rotating, stationary spacetime, emphasizing the distinct roles of gravitational redshift and rotational frame-dragging, motivated by [ ]. Using a covariant formulation based on gauge-invariant phase dynamics and conserved currents within a $$3+1$$ decomposition, we analyze both AC and DC Josephson effects and interferometric configurations. Restricting attention to linear order in the rotation parameter $\textit{a}$, and working in the Eulerian/ZAMO frame, we show that in the slow-rotation slicing adopted here the lapse function agrees with its static (Schwarzschild-type) form up to $$\mathcal {O}(a^2)$$ , while rotational effects enter through the shift vector. Consequently, redshift effects on Josephson frequencies and DC critical currents remain unchanged relative to the non-rotating case at $$\mathcal {O}(a)$$ . The AC Josephson relation retains its redshifted structure when expressed in terms of proper voltages and reduces to the standard flat-spacetime form when formulated in terms of asymptotic (Killing-time) observables. Likewise, the DC critical current measured at infinity scales with a single power of the lapse function and is unaffected by rotation at linear order in the absence of azimuthal condensate momentum. Rotational effects become relevant only in configurations that are sensitive to spatial phase transport or to synchronization with the global time coordinate. In particular, RF-driven interferometric setups can acquire Sagnac-type phase offsets associated with frame dragging, whereas the DC fluxoid constraint remains unshifted at linear order in the present approximation. Our results provide a clean separation between lapse-driven redshift effects and shift-driven rotational contributions in Josephson physics and furnish a consistent framework for superconducting circuits in stationary spacetimes.

Uzbekistan

Nurmukhammed Aytimbetov

Philippines

Reggie Pantig

Türkiye

Ali Övgün

China

Bobomurat Ahmedov

Javlon Rayimbaev

Josephson effects in slowly rotating spacetimes

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.

Nuriddin Kurbonov

Saudi Arabia

Ashfaque H. Bokhari

Muhammad Zahid

Aleksandra Demyanova

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

In this work, we study the gravitational waveforms from the periodic orbits of a massive particle around a dyonic ModMax black hole. We begin with a brief analysis of the spacetime and then examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. In particular, we compute the characteristics of marginally bound orbits and innermost stable circular orbits. Our results show that the values of these quantities increase with the black hole charge $\textit{Q}$ and the screening parameter $$\gamma $$ . We then plot various periodic orbits, characterized by the integers ($\textit{z}$,$\textit{w}$,$\textit{v}$). Finally, we present the gravitational waveforms associated with extreme mass ratio inspirals, consisting of a stellar-mass compact object orbiting a supermassive black hole.

Mirzabek Alloqulov

Azerbaijan

Sanjar Shaymatov

Tao Zhu

Gravitational waveforms from periodic orbits around a dyonic ModMax black hole

The gravitational weak lensing of neutrinos in the presence of a Schwarzschild black hole surrounded by a Dehnen-type dark matter halo is investigated. The event horizon structure is explored, and the existence of the BH is studied in two different slices of the parameter space. Additionally, we derive analytic expressions for the oscillation phase and transition probabilities for both radial and non-radial neutrino propagation. Finally, we use a two-flavor toy model, and numerically analyze how the dark matter halo parameters as density and scale radius, affect oscillation probabilities and examine the role of decoherence. The results show that the presence of a dark matter halo modifies the oscillation phase and damping factor, leading to measurable deviations from the standard Schwarzschild BH case. These findings suggest that neutrino oscillations could, in principle, serve as a probe for dark matter distributions around compact astrophysical objects.

Ahmadjon Abdujabbarov

Chengxun Yuan

Can a Dehnen-type dark matter halo affect the neutrino flavor oscillations?

We investigate the gravitational lensing effects on neutrino oscillations within the framework of Modified Gravity (MOG). By modeling neutrinos as both plane waves and Gaussian wave packets, we analyze how the presence of a massive lensing object between the neutrino source and detector modifies the flavor transition probabilities. In the plane-wave approximation, we derive analytical expressions for lensing-induced interference patterns, showing explicit dependence on the MOG parameter <italic>&#945;</italic>, the impact parameters, and the neutrino mass hierarchy. Extending the analysis to a wave-packet framework, we account for decoherence effects and quantify the damping of oscillation amplitudes due to finite energy and spatial spreads of the wave packets. We compute the decoherence length and damping factor for a realistic Sun-Earth system and demonstrate how both the absolute neutrino mass scale and the MOG parameter influence coherence loss. Our results indicate that gravitational lensing in alternative gravity theories can leave observable imprints on neutrino oscillation patterns, offering a novel probe of both neutrino properties and modifications of General Relativity.

Odilbek Kholmuminov

Bakhtiyor Narzilloev

Pakistan

Ibrar Hussain

Gravitational lensing of neutrinos in the scalar-tensor-vector gravity

In this paper, we investigate periodic orbits exhibiting zoom-whirl behavior around a magnetically charged black hole (MCBH) within the framework of the regular black hole. We examine how the magnetic charge influences orbital dynamics by modifying the background spacetime geometry, thereby affecting the energy and angular momentum of particles. In particular, we calculate the radii of the marginally bound orbits (MBOs) and innermost stable circular orbits (ISCOs), demonstrating that the magnetic charge parameter reduces both radii. This provides valuable insight into the role of the charge parameter in shaping orbital behavior and altering spacetime geometry. We model the complex motion of a stellar-mass object as a timelike particle, inspiraling into a supermassive black hole (SMBH) in the MCBH background, with its trajectory described using periodic geodesic orbits. Based on this analysis of such periodic orbits, we further analyze the gravitational waveforms generated by extreme mass ratio inspirals (EMRIs), in which the SMBH’s spacetime dominates the dynamics of the stellar-mass object. By combining particle trajectory analysis with waveform modeling in a semi-analytical approach, we show that the charge parameter significantly alters the zoom-whirl orbital dynamics and induces notable changes in the waveform structure. These results illustrate that future gravitational wave (GW) observations may constrain the properties of MCBHs, thereby deepening our understanding of the gravitational imprint of regular black holes.

Regular black hole’s impact on the gravitational waveforms from periodic orbits

We investigate the spacetime geometry and astrophysical properties of a static, spherically symmetric black hole in the context of Einstein–Gauss–Bonnet gravity, characterized by a Gauss–Bonnet coupling constant $$\kappa $$ and a non-electromagnetic geometric charge $\textit{Q}$. The black hole solution reduces to the Reissner–Nordstrom or Schwarzschild spacetime in the appropriate limits. We analyze the influence of the parameters $$\kappa $$ and $\textit{Q}$ on the event horizon properties, the innermost stable circular orbit, and the spacetime metric behavior. In the framework of the Novikov–Thorne thin disk model, we compute the flux, temperature, and spectrum of the accretion disk surrounding the black hole. Our results show that the parameters $$\kappa $$ and $\textit{Q}$ significantly affect the disk’s thermal properties and radiation efficiency. Additionally, we demonstrate that the combined effect of these parameters can mimic the role of spin in Kerr black holes, allowing for degeneracy between rotation and geometric corrections. These findings offer potential observational signatures of modified gravity effects in high-energy astrophysical environments.

Ikrom Ergashov

Energetics of accretion disk around black holes in Einstein–Gauss–Bonnet gravity

A novel analytical Schwarzschild-like black hole (BH) solution is derived. It exhibits a static BH with a dark matter (DM) halo characterized by a Dehnen-type density profile. This solution could represent an alternative perspective on the interaction of black hole-dark matter systems, providing new insights into the fundamental properties of DM halos. We study the properties of the newly derived BH solution by examining its spacetime curvature characteristics and energy conditions, providing insights into how the DM halo influences these fundamental characteristics. Additionally, we analyze the timelike geodesics of test particles in the obtained BH-DM spacetime, highlighting how the presence of the novel Dehnen-type DM halo alters the gravitational dynamics and modifies particle trajectories. Increase of the DM halo’s density $$\rho _s$$ and characteristic scale $$r_s$$ leads to an outward shift of both stable and unstable circular orbits. Finally, we test our model by fitting it to real data from the microquasars GRO J1655-40, GRS 1915+105, and XTE J1550-564 using a statistical Markov Chain Monte Carlo (MCMC) method. This allows us to find the best estimates for the properties of the DM halo surrounding these systems.

Uktamjon Uktamov

New analytical model of static black hole with a dark matter halo and parametric constraints through quasiperiodic oscillations

In this work, we explore the vacuum and plasma magnetosphere of a slowly rotating, magnetized neutron star in a conformally coupled scalar field, so-called Bocharova–Bronnikov-Melnikov–Bekenstein (BBMB) geometry. Starting from the vacuum solutions to Maxwell’s equations in a curved spacetime, we derive modified magnetic and electric field structures in the BBMB geometry. We then investigate the behavior of the Goldreich–Julian (GJ) charge density, accelerating electric fields parallel to magnetic field lines, pair production thresholds, and the rate of energy loss through dipolar radiation in the magnetized star. The coupled scalar field significantly enhances magnetic field strength, charge separation, and parallel acceleration, as well as particle acceleration. We also study the deathline conditions that are responsible for secondary pair formation in the BBMB geometry. All results are compared with the general relativistic (GR) limit. As a result, deathline in the $$P-\dot{P}$$ diagram is located above in the spacetime compared with GR frame, implying extended pulsar activity compared to GR. Radiative luminosities from the magnetodipolar radiation process are also increased compared to GR predictions. These findings suggest that BBMB gravity could play a crucial role in shaping the high-energy phenomena of neutron stars and offer new avenues for testing gravity in strong-field regimes.

Sherzod Sayfiyev

Ashfaque Bokhari

Vacuum and plasma magnetosphere around rotating magnetized neutron stars in Bocharova–Bronnikov–Melnikov–Bekenstein geometry

The study of black hole shadows provides a powerful tool for testing the predictions of general relativity and exploring deviations from the standard Kerr metric in the strong gravitational field regime. Here, we investigate the shadow properties of axisymmetric gravitational compact objects using a coordinate-independent formalism. We analyze black hole shadows in various spacetime geometries, including the Kerr, Taub-NUT, $$\gamma $$ , and Kaluza-Klein metrics, to identify distinctive features that can be used to constrain black hole parameters. To achieve a more robust characterization, we employ both Legendre and Fourier expansions, demonstrating that the Fourier approach may offer better coordinate independence and facilitate cross-model comparisons. Finally, we develop a machine learning framework based on neural networks trained on synthetic shadow data, enabling precise parameter estimation from observational results. Using data from observational astronomical facilities such as the Event Horizon Telescope (EHT), Keck, and the Very Large Telescope Interferometer (VLTI), we provide constraints on black hole parameters derived from shadow observations. Our findings highlight the potential of coordinate-independent techniques and machine learning for advancing black hole astrophysics and testing fundamental physics beyond general relativity.

Temurbek Mirzaev

Cosimo Bambi

Exploring black hole shadows in axisymmetric spacetimes with coordinate-independent methods and neural networks