Analyses of astrophysical observations, such as quasiperiodic oscillations (QPOs), combined with theoretical studies, help to understand the deeper properties of black hole spacetime and obtain parameters of black holes and alternative gravity theories. In this study, we investigate the dynamics of charged particles orbiting magnetized black holes within the Bertotti–Robinson (BR) geometry, also known as the electromagnetic universe (EU). We study the circular motion and oscillations of charged particles around a black hole in the presence of a magnetic field, focusing on their applications to QPOs. First, we obtain solutions for the Maxwell equations for orthonormal components of magnetic fields around the black holes in radial and angular directions and analyze the dependence on the EU field and magnetic interactions. The effective potential, specific angular momentum, energy, and innermost stable circular orbits (ISCOs) of charged particles are analyzed to demonstrate how the black hole spacetime, in conjunction with magnetic interaction and EU 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 holes. Furthermore, we investigate twin-peak QPOs using the relativistic precession (RP) model 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 EU, and magnetic interaction parameters, using QPO frequency data observed in microquasars (as an example, XTE J1550-564, GRO J1655-40, GRS 1915+105) and galactic centers (in cases of M82 and Milky Way). Our findings may provide valuable insights into understanding the combined effects of RB spacetime and electromagnetic interactions around black holes on astrophysical observations of QPOs and testing gravity theories in a strong gravity regime.

Uzbekistan

Abubakir Shermatov

Javlon Rayimbaev

Czechia

Bekir Lütfüolu

China

Ahmadjon Abdujabbarov

Sabirov Sardor

Inomjon Ibragimov

Murodbek Vapayev

Bahrom Kuyliev

QPOs analyses and circular orbits of charged particles around magnetized black holes in Bertotti–Robinson geometry

In this paper, we examined the motion of a spinning particle around a Reissner-Nordström-like black hole. Initially, we analyze the dynamics of the spinning test particles using the Mathisson–Papapetrou–Dixon equation. Subsequently, we derive the effective potential and examine it for the parameter of the Reissner-Nordström-like black hole. We then examine the impact of the particle’s spin on the innermost stable circular orbits (ISCO), specific angular momentum, and energy at ISCO for different parameters of hairy black holes. Furthermore, we determine the critical values of the particle’s spin <math altimg='si6.svg'><mi>s</mi></math>, above which time-like particles become non-physical and space-like. Furthermore, we plot and discuss the variation of the critical spin values for different values of <math altimg='si2.svg'><mi>l</mi></math> and charge <math altimg='si3.svg'><mi>Q</mi></math>. Additionally, particle trajectories near a Reissner-Nordstr&#246;m-like (RN-like) black hole are examined for different spacetime and particle parameters. In conclusion, we analyze the center-of-mass of two spinning particles colliding near the boundary of the hairy black hole.

Gulnisa Abdukayumova

Azerbaijan

Farruh Atamurotov

Thailand

Phongpichit Channuie

G. Mustafa

Dynamics of spinning particles around the Reissner-Nordstrom-like black hole

Recently, a study on shadow of quantum corrected Schwarzschild black hole in loop quantum gravity appeared in (Ye et al. in Phys Lett B 851:138566, 2024, ) assuming a fixed value of Barbero–Immirzi parameter $$\gamma $$ . Following this approach, we considered its rotating counterpart being a quantum corrected Kerr black hole in effective loop quantum gravity and studied its deviation from Kerr black hole for a fixed value of $$\gamma $$ . We proposed and proved a theorem describing the location of unstable circular null orbits for all such Kerr-like metrics. The deviation between the shadows of the Kerr and quantum corrected Kerr black holes has also been studied, and the spin parameter is constrained by comparison with the EHT results for M87* and Sgr A* to precisely probe the quantity of deviation due to quantum correction. Lastly, we immersed the quantum corrected Kerr black hole in an inhomogeneous plasma and studied its impact on the shadow size. We found that the unstable null orbits for the quantum corrected Kerr black hole are always smaller than the unstable null orbits for Kerr black hole. The effect of Barbero–Immirzi parameter allows the quantum corrected Kerr black hole to mimic Sgr A* with a higher probability than the Kerr black hole. However, the quantum corrected Kerr black hole does not mimic M87*. The plasma reduces the size of the shadow of quantum corrected black hole, and the plasma parameter in the case II is more sensitive than that in case I.

Pakistan

Muhammad Raza

M. Zubair

Influence of quantum correction on Kerr black hole in effective loop quantum gravity via shadows and EHT results

In this study, we explore metric-Palatini gravity extended by the antisymmetric component of the affine curvature. This gravitational theory results in general relativity plus a geometric Proca field. Building on our previous work, where we constructed its static spherically symmetric solutions in the Anti-de Sitter (AdS) background (Eur. Phys. J. C 83(4):318, 2023), we conduct a comprehensive analysis of the system’s thermodynamics. We examine the thermodynamic properties of the Einstein-Geometric Proca AdS compact objects, focusing on the Hawking temperature, enthalpy, heat capacity, entropy, and Gibbs free energy. Particular attention is given to the dependence of the Hawking temperature, enthalpy, and heat capacity on the uniform potential $$q_1$$ and the electromagnetic-type charge $$q_2$$ . Through numerical analysis, we compute the entropy and Gibbs free energy and investigate how these quantities vary with the model parameters.

Asalkhon Alimova

Türkiye

Elham Ghorani

Israel

Beyhan Puliçe

Thermodynamics of Einstein-Geometric Proca AdS compact objects

We analyze the evolution of perturbations of a (charged) massive scalar field near a regular Simpson-Visser black hole, allowing for a non-zero external magnetic field. We show that the damping rate of the quasinormal frequencies is strongly suppressed by both the magnetic field and the mass term, with indications that arbitrarily long-lived modes, or quasi-resonances, may exist in the spectrum. In the time domain, the quasinormal ringing transitions into slowly decaying oscillatory tails, which are qualitatively distinct from the massive tails observed in the absence of a magnetic field. For nonzero multipole and azimuthal numbers, the power-law envelope characteristic of cases without a magnetic field transforms into an oscillatory envelope that cannot be easily fitted with a simple analytical formula.

Akbar Davlataliev

Bakhtiyor Narzilloev

Ibrar Hussain

Bobomurat Ahmedov

Long-lived quasinormal modes and asymptotic tails of regular Schwarzschild-like black holes in the presence of a magnetic field

The study of spinning charged particle dynamics around black holes in external fields offers insights into relativistic motion and the influence of spin-curvature and electromagnetic interactions. In this work, we investigate the motion of spinning charged test particles in the vicinity of Schwarzschild black holes immersed in asymptotically uniform magnetic fields. Using the Mathisson–Papapetrou–Dixon (MPD) equations, we derive the equations of motion and analyze the superluminal bound, which constrains the physically admissible values of the spin parameter. We investigate how this bound depends on the magnetic interaction parameter $$\omega $$ , which couples the particle’s charge to the external magnetic field. Furthermore, we explore the effective potential and examine how both spin and $$\omega $$ affect circular orbits and the dynamics of the particle. Our results reveal the nonlinear interplay between spin, curvature, and magnetic interaction, contributing to the broader understanding of charged spinning test particle motion in magnetized relativistic environments.

Tursinbay Oteev

Zdeněk Stuchlík

Murat Sharibaev

Circular motion and collisions of charged spinning test particles around magnetized Schwarzschild black hole

An exact analytical solution for the charged traversable wormhole solution has been found by solving minimally coupled Einstein-Maxwell-Scalar (EMS) field equations. It is shown that the spherically-symmetric solution for the charged wormhole of mass <math altimg='si9.svg'><mi>M</mi></math> and charge <math altimg='si8.svg'><mi>Q</mi></math> is represented by the following spacetime metric: <math altimg='si10.svg'><mrow><mi>d</mi><msup><mi>s</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>f</mi><mi>d</mi><msup><mi>t</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><msup><mi>f</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><mrow><mo stretchy='true'>[</mo><mi>d</mi><msup><mi>r</mi><mn>2</mn></msup><mo linebreak='badbreak'>+</mo><msup><mi>r</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>d</mi><msup><mi>&#952;</mi><mn>2</mn></msup><mo linebreak='badbreak'>+</mo><msup><mi>sin</mi><mn>2</mn></msup><mi>&#952;</mi><mi>d</mi><msup><mi>&#981;</mi><mn>2</mn></msup><mo>)</mo></mrow><mo stretchy='true'>]</mo></mrow></mrow></math>, with <display><formula id='ueq0001'><math altimg='si11.svg'><mtable displaystyle='true'><mtr><mtd columnalign='right'><mrow><mi>f</mi><mo linebreak='goodbreak'>=</mo><msup><mrow><mo stretchy='true'>[</mo><mi>cosh</mi><mrow><mo stretchy='true'>(</mo><mfrac><msqrt><mrow><msup><mi>M</mi><mn>2</mn></msup><mo>&#8722;</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></msqrt><mi>r</mi></mfrac><mo stretchy='true'>)</mo></mrow><mo>+</mo><mfrac><mi>M</mi><msqrt><mrow><msup><mi>M</mi><mn>2</mn></msup><mo>&#8722;</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></msqrt></mfrac><mi>sinh</mi><mrow><mo stretchy='true'>(</mo><mfrac><msqrt><mrow><msup><mi>M</mi><mn>2</mn></msup><mo>&#8722;</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></msqrt><mi>r</mi></mfrac><mo stretchy='true'>)</mo></mrow><mo stretchy='true'>]</mo></mrow><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup><mspace width='0.16em' /></mrow></mtd></mtr></mtable></math></formula></display>which covers the well-known Papapetrou &#8220;exponential&#8221; metric for the uncharged wormhole. It is also shown that the obtained result is the regular solution of EMS field equations. Along the solution we have presented overcharged naked singularity with <math altimg='si3.svg'><mrow><mi>Q</mi><mo linebreak='goodbreak'>&gt;</mo><mi>M</mi></mrow></math>. As a probe of the spacetime metric, the geodesic motion has been investigated. The innermost stable circular orbit of test particle has been studied.

Bobur Turimov

Exact charged traversable wormhole solution

We investigate the dynamics of spinning test particles orbiting static black holes in effective quantum gravity (EQG) using the Mathisson–Papapetrou–Dixon (MPD) formalism with two distinct models. The purpose of using two models is to compare qualitatively different realizations of EQG corrections and assess their impact on spin-gravity coupling and orbital behavior. Through analysis of the effective potential, we demonstrate how $$\zeta $$ and particle spin $\textit{s}$ jointly influence orbital stability, revealing that (i) in Model-1, increasing $$\zeta $$ elevates the potential barrier while spin effects become dominant near the horizon, (ii) Model-2 shows weaker dependence on $$\zeta $$ except for high-spin configurations. The innermost stable circular orbits (ISCOs) exhibit characteristic scaling $$r_{\text {ISCO}}(\zeta ,s)$$ , with quantum corrections that increase the radius of the ISCO by up to 27% relative to Schwarzschild for $$\zeta =4$$ in Model-1. We derive critical spin values $$s_{\text {max}}$$ beyond which particle trajectories become spacelike, finding $$s_{\text {max}}$$ decreases monotonically with $$\zeta $$ in Model-2 but shows non-monotonic behaviour in Model-1. The particle collision energetics are analyzed, showing that the center-of-mass energies $$E_{\text {cm}}$$ can be enhanced by spin-parameter tuning, reaching $$E_{\text {cm}}/2m \sim 8$$ for $$(\zeta ,s_1,s_2)=(4,-0.5,0.5)$$ near the horizon. Trajectory simulations reveal that quantum corrections in Model-1 induce precession effects absent in Model-2, suggesting observational signatures to distinguish EQG models. Our results establish the combined influence of quantum spacetime structure and spin-curvature coupling on the test particle dynamics, with implications for EQG phenomenology and gravitational wave astronomy.

Dilmurod Umarov

South Africa

India

Sushant Ghosh

Dynamics of spinning particles around static black holes in effective quantum gravity

Studying black holes in alternative gravitational frameworks is crucial for understanding the interplay between dark matter and modified gravity. This work examines black holes immersed in perfect fluid dark matter (PFDM) within the Kalb–Ramond (KR) gravity framework. The KR field, a rank-2 antisymmetric tensor, introduces additional degrees of freedom that alter spacetime geometry and affect particle dynamics. We derive the metric for a black hole embedded in PFDM and analyze the circular motion of test particles. By investigating the effective potential, energy, and angular momentum, we determine conditions for stable circular orbits and explore the impact of KR field parameters and PFDM properties. Beyond kinematics, we study quasi-periodic oscillations (QPOs) commonly observed in the X-ray spectra of black hole accretion disks. We link QPO frequencies to orbital properties in our model, proposing an observational test to distinguish KR gravity with PFDM from general relativity. Additionally, we explore the thermodynamic aspects of these black holes, calculating temperature, entropy, and heat capacity to assess the impact of the KR field and PFDM on stability and phase transitions. Radiation properties are also investigated, including modifications to radiation due to the influence of the PFDM and the KR field on the event horizon. Our results reveal that KR gravity and PFDM generate distinctive signatures in particle dynamics, QPO patterns, thermodynamics, and radiation, offering potential observational tests to differentiate these models from standard general relativity (GR).

Shokhzod Jumaniyozov

Sardor Murodov

Bekzod Madaminov

Sharofiddin Urinbaev

Black holes surrounded by PFDM in Kalb-Ramond gravity: from thermodynamics to QPO tests

In this paper, we investigate the dynamics of the neutral and charged test particles together with the radiation properties of an accretion disk around the charged hairy black hole. Firstly, we briefly overview the spacetime of the charged hairy BH and explore the horizon structure. Then we study the effect of the spacetime parameters on the motion of massive neutral and charged particles. Finally, we explore the radiation properties of the charged hairy BH using the Novikov–Thorne model. The important quantities are analyzed: the flux of electromagnetic radiation, the temperature of the accretion disk, and the differential luminosity. The parameters $$\alpha $$ and $\textit{l}$ are found to decrease the flux of electromagnetic radiation, while the BH charge $\textit{Q}$ increases it. Similarly, the disk temperature and differential luminosity decrease owing to the impact of the $$\alpha $$ and $\textit{l}$ parameters, and increase due to the BH charge $\textit{Q}$.

Mirzabek Alloqulov

Chengxun Yuan

Chen Zhou

Particle dynamics and accretion disk radiation around charged hairy black holes