Scalar–tensor theories of gravity provide a natural extension of general relativity and may predict naked singularities as alternative compact objects. In this work, we investigate a novel exact solution within the Freud–Nambu scalar–tensor gravity framework, generalizing the Janis–Newman–Winicour (JNW) naked singularity spacetime through the introduction of a parameter q coupled to a real scalar field φ with mass μ. Although the metric remains identical to the JNW solution, the scalar field profile is modified, providing a parametrized deformation of this class of spacetimes. We analyze particle dynamics in this background, including a direct linear coupling between the test particle and the scalar field characterized by the parameter g_s. The influence of these parameters on astrophysical observables is studied through the specific angular momentum, the innermost stable circular orbit (ISCO), and the radiative efficiency of accretion. We also derive the epicyclic frequencies governing oscillatory motion and explore their implications for quasi-periodic oscillations (QPOs) in black hole binaries. Within the epicyclic resonance model, the upper and lower QPO frequencies depend sensitively on the parameters n, g_s, and q. To constrain the model, we perform a Markov Chain Monte Carlo analysis using twin-peak QPO data from the microquasars XTE J1550–564 and GRS 1915+105. The resulting black hole masses agree with previous estimates and provide the first observational constraints on the parameters q and g_s, indicating that modified gravity effects may leave detectable imprints on strong-field astrophysical phenomena.

We investigated the dipolar magnetic field generated by a static current loop around a compact gravitational source described by the exponential metric. Starting from Maxwell’s equations, we derived the expression for the electromagnetic vector potential in this spacetime and obtained analytical solutions. The angular dependence of the vector potential is expressed through Legendre polynomials, while the radial part is represented by the hypergeometric function of the first kind. The integration constants were determined by enforcing the continuity of the vector potential at the location of the source and by substituting the solution back into Maxwell’s equations. The resulting magnetic field is uniform in the interior region, resembling the Wald solution, whereas in the exterior region it assumes a dipolar structure. Moreover, the external magnetic field strength decreases with increasing radial distance. We have investigated the effect of introducing a dipole magnetic field on the motion of charged particles around the compact object. Our results show that the presence of this magnetic field alters the particle dynamics and causes the radius of the innermost stable circular orbit (ISCO) to move outward compared with the case of a neutral particle.

In this paper, we explored novel feature of the Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole by analyzing geodesic motion. We first examined its thermodynamics and showed that Hawking temperature equals to zero. We investigated motion of both massive and massless particles around the BBMB black hole and studied the characteristic radii, namely, marginally stable circular orbit (MSCO) and marginally bound orbit (MBO) for massive particles orbiting the BBMB black hole. Additionally, we found that the energy efficiency of massive particles in the BBMB spacetime can reach up to 8%. We also studied the capture cross section of massless (photon) and massive particles by the BBMB black hole. From the equations of motion, we derived the radial function crucial for determining the critical value of the impact parameter for photons and particles. Comparing these findings with the Schwarzschild spacetime, we observed significant differences in gravitational properties. Specifically, the impact parameter for a photon is smaller in the Schwarzschild field than in the BBMB field, indicating weaker gravity around the BBMB black hole, as corroborated by the closer location of the photon sphere in the BBMB spacetime. We derived explicit expressions for the pericentric precession and the deflection angle of light by the BBMB black hole, along with the trajectory of massive particles orbiting the black hole. We showed that test particles on elliptical trajectories experience pericenter shifts, with pericentric precession in the BBMB spacetime being slightly less than that predicted by Einstein's general theory of relativity. Lastly, we studied the deflection of light rays and gravitational lensing effects by the BBMB black hole in both strong and weak field approximations, incorporating general relativistic effects from the Schwarzschild spacetime. We derived expressions for the deflection angle in first and second order approximations, and used the gravitational lensing equation to determine the magnification of primary and secondary images.

We have presented a solution for a charged Zipoy-Voorhees metric within the framework of low-energy effective field theory for heterotic string theory. This exact solution represents a deformed gravitational field in four-dimensional spacetime, characterized by three key parameters: the mass M, the electric charge Q, and the deformation parameter y, which controls deviations from spherical symmetry. Unlike standard black hole solutions, this metric describes a naked singularity, meaning it lacks an event horizon and exposes the central singularity to external observers. To examine the physical properties of this spacetime, we analyzed the geodesic motion of test particles and photons. The study of geodesic trajectories provides insight into the effects of the deformation parameter y and charged parameter b = Q2/2M on orbital motion, shadow, and potential astrophysical observables. Finally, a constraint on charge and deformation parameter using observed shadow radius of M87* has been obtained.

We have studied neutral and charged massive particles dynamics in Ellis spacetime in the presence of the external scalar field. Focusing on the circular motion of massive particles, the impact of an external scalar field on the Innermost Stable Circular Orbit (ISCO) position is analysed, revealing a non-linear relationship with the scalar field parameter. Perturbation techniques are employed to investigate oscillatory motion near stable orbits in the Ellis spacetime, yielding analytical expressions for radial and angular oscillations. The throat of the wormhole has been constrained by comparing theoretical and observational results for fundamental frequencies of particles from quasars. Finally, scalar and gravitational perturbations in the Ellis spacetime have been studied. It is shown that the equation for the scalar profile function is fully independent from the tensor functions and the solution can be represented in terms of the confluent Heun function. However, it has been shown that equations for the tensor profile functions strongly depend on the scalar profile functions in the Ellis spacetime and they are reduced to the Regge- Wheeler-Zerilli equation. Finally, numerical solutions to the Regge-Wheeler-Zerilli equation for the radial functions in the Ellis have been presented.

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 M and charge Q is represented by the following spacetime metric: ds2=−fdt2+f−1[dr2+r2(dθ2+sin2θdϕ2)], withf=[cosh(M2−Q2r)+MM2−Q2sinh(M2−Q2r)]−2which covers the well-known Papapetrou “exponential” 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 Q>M. As a probe of the spacetime metric, the geodesic motion has been investigated. The innermost stable circular orbit of test particle has been studied.

We examine the tidal forces exerted by the Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) black hole and analyze their behavior. Our findings indicate that the radial and angular components of these forces can take both positive and negative values near the black hole, depending on the spacetime parameters. Unlike the Schwarzschild black hole, where the radial tidal force always stretches and the angular tidal force always compresses—both diverging at the event horizon—the BBMB black hole allows for finite tidal forces that can either stretch or compress within the event horizon. Furthermore, we derive the geodesic deviation equations for a freely falling particle and solve them numerically. Our results reveal that the initial position has opposing effects on the magnitudes of the physical quantities related to tidal forces.

In the paper (D. Senjaya, 2024 [1]), the author investigated the massless spinor field in the Schwarzschild spacetime and derived an analytical solution expressed in terms of the Heun function. However, based on this approach, an incorrect expression for the solution to the Dirac equation was derived, leading to an erroneous result. Subsequently, in the comment paper (R.R.S. Oliveira, 2024 [2]), it was explicitly pointed out that the Fock-Ivanenko coefficients had been overlooked, and a correct derivation of the Dirac equation in Schwarzschild spacetime was provided. In this note, we have demonstrated that the explicit form of the Dirac equation in both the original and comment papers is the same. Furthermore, we have shown that obtaining an analytical solution to the Dirac equation in Schwarzschild spacetime is not possible.

In this work, we investigate static configurations of dark energy stars within the framework of Rastall-Rainbow (R-R) gravity, which combines an energy-dependent deformation of spacetime with a nonminimal coupling between matter and geometry. We begin by deriving the modified field equations corresponding to R-R gravity and subsequently reformulate the stellar structure equations to describe hydrostatic equilibrium. The generalized Tolman-Oppenheimer-Volkoff (TOV) equations are then solved numerically by adopting the modified Chaplygin equation of state to model the interior matter distribution. The R-R parameters, along with fluid constants, are shown to influence the maximum mass, radii, and stiffness of the star sequences compared to the baseline set by general relativity. We apply observational benchmarks from high-mass pulsars and binary-merger events (e.g., GW170817 and GW190814) to appraise viability within the explored parameter space. The results collectively suggest that stable, causal configurations arise from physically meaningful parameter selections, with deviations from general relativity leading to systematic changes in structural characteristics while adhering to theoretical limits. These findings illustrate that Rastall-Rainbow gravity can support stable, observationally consistent dark energy stars, providing verifiable signatures in strong gravitational fields.

We have studied the motion of massive particles under the influence of scalar and gravitational fields, with particular emphasis on the BBMB black hole. It has been shown that the radius of the innermost stable circular orbit (ISCO) and marginally bound orbit are significantly affected by the scalar coupling parameter. We study the energy efficiency of thin accretion disks around BBMB black holes, showing that the efficiency decreases for positive gs and increases for negative gs, with a maximum of approximately 30% for specific gs values. We derive analytical expressions for the angular and linear velocities of orbiting particles, highlighting their dependence on gs. The photon sphere is shown to be independent of gs, but the linear velocity at the ISCO position varies significantly, with massive particles behaving like ultra-relativistic particles near the black hole under scalar field influence. Additionally, we examine the center-of-mass energy (CME) of colliding particles near the BBMB black hole, showing that the scalar field can lead to infinitely high CME near the horizon, consistent with the BSW process. Astrophysical implications include CME values reaching 1020eV, comparable to the energies of ultra-high-energy cosmic rays (UHECR).

We demonstrate that the Curzon metric for a positive mass configuration possesses a singular event horizon with infinite area. This singularity has significant implications, revealing that the three-dimensional spatial hypersurfaces, which are orthogonal to the Killing vector field, exhibit a multiply connected structure. Furthermore, we investigate the dynamics of a test particle orbiting a central γ-object within this spacetime. It is found that under certain conditions, the particle's velocity can approach the speed of light, leading to an exceptionally high total energy at a specific value of the deformation parameter governing the spacetime structure. Moreover, we uncover a causality issue for a critical value of the deformation parameter, where the test particle can exceed the speed of light, potentially offering new insights into the theoretical existence of tachyons. This study contributes to the understanding of relativistic objects in deformed spacetimes and suggests that such violations of causality could play a role in explaining the elusive nature of tachyonic phenomena in high-energy physics.

In this paper, we investigated the motion of massive particles in the presence of scalar and gravitational fields, particularly focusing on the Janis-Newman-Winicour (JNW) naked singularity solution. It is shown that the innermost stable circular orbit (ISCO) radius strongly depends on scalar coupling parameter. Additionally, we explored the radiation reaction effects on particle dynamics, incorporating a reaction term into the motion equations. Numerical simulations indicated minimal impact on particle trajectories from radiation reaction. We also examined the oscillatory motion of particles around compact objects in the JNW spacetime, focusing on radial and vertical oscillations. Our analysis indicated that the scalar field's coupling parameter and the spacetime deformation parameter $n$ significantly alter the fundamental frequencies of these oscillations. Furthermore, we studied quasi-periodic oscillations (QPOs) in X-ray binaries, using the relativistic precession (RP) model to analyze upper and lower frequency relationships. Our results indicated that increasing parameters ($n$ and $g_s$) shifts the frequency ratio of 3:2 QPOs closer to the naked singularity, with $n$ decreasing and $g_s$ increasing both frequencies. Finally, we analyzed QPO data from selected four X-ray binary systems using Markov Chain Monte Carlo (MCMC) analysis to constrain JNW parameters. Our findings provided insights into the mass, coupling and deformation parameter for each system, enhancing our understanding of compact object dynamics in strong gravitational fields.

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data.

AbstractAccretion 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.

We consider the collision of two particles having distinct rest masses and orbiting near a Kerr-MOG black hole, and we further determine the center-of-mass energy (i.e., CME) associated with the particles. It is found that the CME energy is influenced not only by the rotation parameter a , but also by the MOG parameter α . Notably, it is shown that an extremal Kerr-MOG black hole case leads to surprisingly high the CME if and only if the parameter a satisfies the values given in the range (0,√(1+α)) which diverges from that observed in Kerr-like black holes, thus highlighting the distinct characteristics of Kerr-MOG black holes. We present compelling evidence suggesting that Kerr-MOG black holes potentially act as significant generators for high-energy particles within the polar region.

According to the Banados-Silk-West (BSW) process, rotating black holes can act as particle colliders capable of achieving arbitrarily high center-of-mass energy (CME), provided that a specific angular momentum of one of the particles is present. In this discussion, we demonstrate that both Kerr black holes and Schwarzschild black holes could serve as potential sources of high-energy particles in the polar region.

The paper has explored analogue of gravitational synchrotron massive particle and Penrose process in MOdified Gravity (MOG) known as Scalar-Tensor-Vector-Gravity (STVG). Investigation of the gravitational field around Kerr-MOG black hole showed that it has strong gravitational field with large horizon and can rotate faster than Kerr black hole due to the effect of STVG. We have studied influence of STVG in circular motion of massive particle around Kerr-MOG black hole and discussed the Innermost Stable Circular Orbit (ISCO) of massive test particle. It is shown that STVG plays a crucial role in energy extraction from a rotating black hole, with an energy efficiency of more than 100% according to the Penrose process. Furthermore, we have explored the gravitational synchrotron radiation analogue produced by a massive particle orbiting around a Kerr-MOG black hole. It has been shown that the intensity of gravitational radiation from binary systems of stellar black holes (SBH) and supermassive black holes (SMBH).

The electrodynamics of the highly magnetized and spherical symmetric neutron star within the framework of special relativity has been investigated. It is assumed that the neutron star is isolated and consists of highly conducting matter. Explicit demonstrations were made regarding the multipole solutions for both axially symmetric and non-axially symmetric electromagnetic fields surrounding the neutron star. It was observed that the axially symmetric solutions are independent of time, whereas the non-axially symmetric solutions are time-dependent. Additionally, wave-like solutions for the electromagnetic field in TE and TM modes were derived.

We study matter accretion in a static, axially symmetric and vacuum geometry describing the exterior gravitational field of a black hole mimicker called the γ metric. We evaluate the thermal and optical properties of thin accretion disks, including the emission rate, luminosity and shadow, in the gamma spacetime. Also, we explore the radial accretion of polytropic matter fields onto the central source and evaluate the thermal and optical properties of the infalling gas, such as temperature and luminosity. The results are discussed in the context of evaluating the possibility that the true nature of astrophysical black hole candidates may not be a black hole but some exotic compact object possessing a non-vanishing mass quadrupole moment.