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.

Uzbekistan

Sherzod Sayfiyev

Saudi Arabia

Ashfaque Bokhari

China

Bobomurat Ahmedov

Javlon Rayimbaev

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

In our previous papers we have analyzed the stability of vacuum and electrovacuum static, spherically symmetric space-times in the framework of the Bergmann–Wagoner–Nordtvedt class of scalar-tensor theories (STT) of gravity. In the present paper, we continue this study by examining the stability of exceptional solutions of the Brans–Dicke theory with the coupling constant $$\omega =0$$ that were not covered in the previous studies. Such solutions describe neutral or charged wormholes and involve a conformal continuation: the standard conformal transformation maps the whole Einstein-frame manifold $${\mathbb {M}}_\textrm{E}$$ to only a part of the Jordan-frame manifold $${\mathbb {M}}_\textrm{J}$$ , which has to be continued beyond the emerging regular boundary S, and the new region maps to another manifold $${\mathbb {M}}_\textrm{E}$$ $${}_{-}$$ . The metric in $${\mathbb {M}}_\textrm{J}$$ is symmetric with respect to S only if the charge $\textit{q}$ is zero. Our stability study concerns radial (monopole) perturbations, and it is shown that the wormhole is stable if $$q \ne 0$$ and unstable only in the symmetric case $$q=0$$ .

Russia

Kirill Bronnikov

Sergei Bolokhov

Milena Skvortsova

Rustam Ibadov

Feruza Shaymanova

On the stability of exceptional Brans–Dicke wormholes

In this paper, we present a spherically symmetric wormhole in Einstein gravity coupled with the phantom scalar field and the nonlinear electromagnetic field. Numerical results show that this solution violates the Null Energy Condition (NEC), and as the parameters change, the ADM mass of the entire spacetime changes from positive to negative. In addition, we analyze the light ring (LR) of the solution and demonstrate the astronomical observation properties. Especially when negative mass appears, the general LR will not appear, only a “special unstable LR” exists at the throat, which is caused by the repulsive effect of the negative mass on both sides of the wormhole. Finally, we draw the embedding diagram to reflect the geometric characteristics of the wormhole.

Xin Su

Chen-Hao Hao

Tie-Feng Fang

Yong-Qiang Wang

Generalized Bronnikov–Ellis wormhole with nonlinear electromagnetic field

Testing gravity theories beyond General Relativity (GR) is crucial for a deeper understanding of fundamental physics, especially in the strong gravitational field regime around astrophysical compact objects. This work examines quasi-periodic oscillations (QPOs) generated by charged particles orbiting magnetized Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) black holes. We study charged particles’ circular orbits, deriving expressions for energy and angular momentum influenced by scalar and magnetic interactions, and investigate the innermost stable circular orbit (ISCO). Using the relativistic precession (RP) model, we derive the fundamental orbital, radial, and vertical frequencies of charged particle oscillations, highlighting deviations caused by conformal scalar and magnetic interactions. Our analysis shows that the conformally coupled scalar field significantly modifies the spacetime curvature, producing a repulsive gravitational effect that shifts stable orbits outward, thereby reducing the radial oscillation frequency. Using observational QPO data from well-known astrophysical sources-GRS 1915+105, GRO J1655-40, M82 X-1, and Sgr A*-we performed Markov Chain Monte Carlo (MCMC) simulations to constrain black hole mass, scalar coupling, magnetic interaction, and orbital radius parameters. Our results reveal significant deviations from standard General Relativity predictions, offering clear evidence of scalar and magnetic field influences. These findings indicate that scalar and magnetic fields produce observable shifts in QPO frequencies, providing promising observational signatures to test alternative gravitational theories in extreme astrophysical environments.

Sardor Murodov

QPOs tests and circular motions of charged particles around magnetized Bocharova–Bronnikov–Melnikov–Bekenstein black holes

In this study, we investigate the motion of magnetized particles around a Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) black hole in an external magnetic field, emphasizing the effects of an external magnetic field and a conformally coupled scalar field. We analyze the properties of circular orbits, the innermost stable circular orbit (ISCO), and the dynamics of high-energy particle collisions, focusing on the center-of-mass energy (CME) of colliding particles. We derive the equations governing the motion of magnetized particles in the BBMB spacetime and explore how the scalar coupling and the magnetic-dipole interaction parameters influence orbital stability and collision energetics. Our findings reveal that the ISCO radius is significantly modified by both scalar and magnetic interactions, leading to shifts in stability conditions and variations in the angular momentum requirements. The study also demonstrates that the critical angular momentum, which determines the transition between bound and unbound motion, is reduced compared to the Schwarzschild case due to the influence of the conformal scalar field. One key result is that the CME of colliding magnetized particles can be significantly enhanced in the BBMB spacetime. Increasing magnetic interaction and a stronger attractive scalar field lead to higher CME values, making the BBMB black hole a potential site for high-energy astrophysical processes. This suggests that external magnetic fields and scalar interactions play a crucial role in energy extraction mechanisms and the formation of ultrarelativistic particles.

Nuriddin Kurbonov

Circular orbits and collisions of particles with magnetic dipole moment around magnetized Bocharova–Bronnikov–Melnikov–Bekenstein black holes

In this paper, we theoretically investigate gravitational lensing within the space-time framework of traversable wormholes, focusing on the combined effects of a global monopole and a cosmic string. Specifically, we examine the Ellis-Bronnikov-Morris-Thorne wormhole metric and analyze how these topological defects influence photon trajectories. By considering the weak-field limit, we derive analytical expressions for the photon deflection angle, highlighting how factors such as the wormhole throat radius, the global monopole charge, and the cosmic string influence the gravitational lensing phenomenon. We also examine the weak-field limit of lensing phenomena for a zero wormhole throat radius and derive an analytical expression for the deflection angle of photon light in this scenario.

India

Faizuddin Ahmed

Türkiye

İzzet Sakallı

Jordan

Ahmad Al-Badawi

Gravitational lensing phenomena of Ellis-Bronnikov-Morris-Thorne wormhole with global monopole and cosmic string

Accretion processes near black hole candidates are associated with the high-energy emission of radiation from relativistic particles and outflows. It is widely believed that the magnetic field plays a crucial role in explaining these high-energy processes near these astrophysical sources. In this work, we analyze thin accretion disks in the Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) spacetime framework using the Novikov–Thorne model. Our study examines the thermal and optical characteristics of these disks, including their emission rate and luminosity in the specified spacetime. Later, we extend the Novikov–Thorne model to ionized thin accretion disk. We propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamics of charged particles near a weakly magnetized black hole. Our findings show that, in the presence of a magnetic field, the radius of the marginally stable circular orbit (MSCO) for a charged particle is close to the black hole’s horizon. The orbital velocity of the charged particle, as measured by a local observer, has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiation emitted by the accelerating relativistic charged particle orbiting the magnetized black hole.

Bobur Turimov

Akbar Davlataliev

Yusuf Usmanov

Shavkat Karshiboev

Pulat Tadjimuratov

Investigating new aspects of Bocharova–Bronnikov–Melnikov–Bekenstein spacetime: ionized thin accretion disk model

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter  $$\xi $$  <math> <mi>ξ</mi> </math>  . The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

On the stability of electrovacuum space-times in scalar–tensor gravity

One of the main issues in gravitation is the presence of singularities in the most common space-time solutions of General Relativity, as the case of black holes. A way of constructing regular solutions that remove spacelike singularities consists in implement a bounce on such space-time, leading to what is usually known as black bounce space-times. Such space-times are known to describe regular black holes or traversable wormholes. However, one of the main issues lies on reconstructing the appropriate source that leads to such a solution. In this paper, a reconstruction method is implemented to show that such types of metrics can be well accommodated in non-linear electrodynamics with the presence of a scalar field. Some of the most important black bounces solutions are reconstructed in this framework, both in 3 + 1 as in 2 + 1 dimensions. For the first time in the literature, these solutions have an electrically charged source of matter from non-linear electrodynamics. Specific features are indicated that distinguish electric sources from magnetic ones, previously found for the same space-times.

Brazil

G. Alencar

Manuel Rodrigues

Spain

Diego Gómez

Marcos Silva

On black bounce space-times in non-linear electrodynamics

In this letter, we investigate behaviour of massive and massless scalar field that is represented by the covariant Klein–Gordon equation with Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) black hole background. We successfully solve analytically the governing relativistic wave equation and discover the exact quasibound states’ wave functions and energy levels of both massive and massless cases. The corresponding quasibound states have complex-valued energy  $$E=E_R+iE_I$$  <math> <mrow> <mi>E</mi> <mo>=</mo> <msub> <mi>E</mi> <mi>R</mi> </msub> <mo>+</mo> <mi>i</mi> <msub> <mi>E</mi> <mi>I</mi> </msub> </mrow> </math>   where the real part  $$E_R$$  <math> <msub> <mi>E</mi> <mi>R</mi> </msub> </math>   can be interpreted as the scalar’s relativistic quantized energy while the imaginary part represents decay as the quasibound states tunnels through the black hole’s horizon. The Hawking radiation coming out of the BBMB black hole’s horizon is also discussed and calculated via the Damour–Ruffini method, i.e. by singling out the particle–anti-particle parts of the obtained exact scalar’s exact wave function from where, the radiation distribution function is derived and the Hawking temperature is obtained.

Thailand

David Senjaya

The Bocharova–Bronnikov–Melnikov–Bekenstein black hole’s exact quasibound states and Hawking radiation