This study examines the black hole developed from multi-polytropic equations of state by investigating particle dynamics and various related properties, such as the radius of the horizon, the effective force, the innermost stable circular orbit radius, the photon radius, quasi-periodic oscillations, and the weak plasma lensing in uniform plasma fields, singular isothermal sphere (SIS), and non-singular isothermal gas sphere (NSIS). Furthermore, we examine the image magnification for the black hole solution. An important parameter in this black hole solution is $$c_1$$ , which significantly impacts the results. Our study shows that particle dynamics features and deflection of light are affected by the black hole parameter.

Azerbaijan

Pakistan

Allah Ditta

China

Farzan Mushtaq

Thailand

Phongpichit Channuie

Saudi Arabia

Awad Ibraheem

Asifa Ashraf

India

Rana Zulqarnain

Studying the properties of particle motion and plasma lensing in regular black holes from multi-polytropic equations of state

This study investigates the existence and stability of traversable wormhole (WH) solutions within the framework of Rastall Teleparallel Gravity. In this context, we focus on the impact of geometric constraints and energy conditions. Utilizing the class I embedding technique under the Karmarkar condition, we derive two novel static spherically symmetric WH solutions. In addition, these solutions are illustrated with distinct redshift functions, leading to corresponding shape functions that satisfy the Morris-Thorne criteria, ensuring asymptotic flatness and necessary throat conditions. The field equations, constructed within an anisotropic stress-energy tensor framework, are analyzed to evaluate the energy density, radial pressure, and tangential pressure distributions. A comprehensive graphical analysis tested the energy conditions, i.e., the null energy condition (NEC), weak energy condition (WEC), strong energy condition (SEC), and dominant energy condition (DEC). This shows the violations of the Null Energy Condition (NEC), confirming the presence of exotic matter necessary for sustaining WH structures. Both models exhibit regions where the energy density remains positive, while radial and tangential pressures violate classical energy conditions, reinforcing the theoretical expectations for the stability of the WH. Also, these results illustrated the compatibility of Rastall Teleparallel Gravity with traversable WH subjects and tested the intricate matter-geometry interplay in exotic spacetimes.

Amna Saleem

Zulfiqar Ali

Algeria

Abdelmalek Bouzenada

Uzbekistan

Farruh Atamurotov

G. Mustafa

New relativistic traversable wormholes and energy constraints in the rastall teleparallel gravitational paradigm

This study investigates the deflection of light, Einstein rings, thermal fluctuations, and tidal force and geodesic deviation in a loop quantum black hole (LQBH) resulting from gravitational collapse. Initially, we employ the Gauss–Bonnet theorem (GBT) to examine the weak deflection angle of the LQBH. For the GBT, we used the Gibbons-Werner method to obtain the Gaussian optical curvature. We also determined the deflection angle for a spherically symmetric BH in the context of the non-plasma and plasma environments under weak field constraints. Furthermore, we graphically investigate the deflection angle of light in the scenario of the impact parameter and find that the impact parameter has a direct effect on the angle. Later, we compute the Einstein rings of the LQBH and examine the graphical impact of various parameters. Moreover, we employ corrected entropy to examine the effects of thermal fluctuations for small and large BHs. For both large and small BHs, we examine the impact of the correction terms on the thermodynamic system. We also study the geodesic deviation in LQBH, with a particular emphasis on how quantum factors affect the paths of neighboring geodesics. Angular geodesics, in contrast to radial geodesics, tend to converge as one moves away from the BH, a phenomenon that reflects the complicated consequences of space-time curvature in this scenario.

Xia Tiecheng

Faisal Javed

Bander Almutairi

Abdullo Hakimov

Impact of loop quantum gravity on gravitational lensing, thermal fluctuations, tidal force and geodesic deviation around a black hole

We investigate the dynamics of test particles around a spherically symmetric, non-rotating, hairy regular black hole, examining how the model parameters affect particle motion. The black hole is characterized by two parameters, the mass $$M$$ and a hairy parameter $$\alpha $$ . Using the effective potential, we examine the stability of circular orbits. We derive analytical expressions for the energy and angular momentum of test particles as a function of the black hole parameters. The effective forces acting on particles and the innermost stable circular orbits are also examined. Additionally, we numerically integrate the equations of motion to examine particle trajectories and further investigate their motion. Epicyclic oscillations of test particles close to the equatorial plane are explored, and analytical expressions for radial, vertical, and orbital frequencies are derived as functions of the black hole parameters. We also examine the frequency of periastron precession of the particles. We compare the motion of test particles around a hairy regular black hole with the particle motion around a classical non-rotating Schwarzschild black hole. Further, we discuss thermally fluctuating phenomena by using the Tsallis entropy and the energy emission process. Our findings show that the black hole model’s parameters significantly impact particle motion and thermal features.

Tayyab Naseer

Oman

S. Maurya

Saibal Ray

Testing of QPOs, particle dynamics, emission energy and thermal fluctuation around a regular hairy black hole

We investigate the matter accretion of well-known fluids flowing onto a Schwarzschild-like black hole in Einstein–Grisaru–Zanon (EGZ) gravity. Within the framework of EGZ gravity, we can determine the accretion properties of fluids that have been extensively studied, including ultra-stiff fluid (USF), ultra-relativistic fluid (URF), radiation fluid (RF) and sub-relativistic fluid (SRF) by employing the dynamical approach. In this perspective, we have considered the steady-state and spherically symmetric accretion onto a Schwarzschild-like black hole in EGZ gravity. For this purpose, we have classified the isothermal types of fluid in the context of equations of state (EOS). Moreover, we have introduced the polytropic test fluid with accretion disks. The mass accretion rate is also investigated near a Schwarzschild-like black hole in EGZ gravity. It is interesting to note that the mass accretion rate of the Schwarzschild-like black hole in EGZ gravity exhibits a more typical behavior than the ordinary Schwarzschild black hole, which has been presented graphically under the effect of the involved black hole parameters. Furthermore, we have observed that the parameter involved in $$\gamma $$ influences the properties of accretion near a black hole horizon.

Accretion onto a Schwarzschild-like black hole in Einstein-Grisaru-Zanon gravity

We investigate the dynamics of test particles around a spherically symmetric, non-rotating hairy-Bardeen black hole, and then study the influence of the model’s parameters on the particle motion. The black hole is fully characterized by five parameters, the mass $\textit{M}$ of the black hole, the charge $\textit{Q}$ of the black hole, coupling constant $$\beta $$ , the parameter $$\gamma $$ describing the hair of the black hole, and a BH parameter $$\eta $$ . Using the effective potential technique, we study the stability and instability of circular equatorial orbits. We calculate the analytical expressions for the energy and angular momentum of test particles as functions of black hole parameters. The effective forces acting on particles as well as the innermost stable circular orbits have also been studied. Epicyclic oscillations of test particles close to the equatorial plane are explored, and analytical expressions for radial, vertical, and orbital frequencies have been derived. We also investigated the frequency of periastron precession of the particles. We also study the thermal properties showing the emission rate of energy and thermal fluctuation by calculating the Hawking temperature. Our findings reveal that the black hole model’s parameters significantly impact particle motion.

Circular motion, QPOs testing, emission energy and thermal fluctuations around a non-singular hairy Bardeen black hole

This study examines the regular charged black hole solution by investigating particle dynamics and various related properties, such as the radius of the horizon, the effective force, the energy, the angular momentum, the ISCO radius, the photon radius, the red-blue shift, and the weak plasma lensing in uniform plasma fields, <italic>SIS</italic>, and <math altimg='si1.svg'><mi>N</mi><mi>S</mi><mi>I</mi><mi>S</mi></math>. Furthermore, we examine the image magnification for the black hole solution. A salient characteristic of this black hole solution is the incorporation of the magnetic charge parameter <italic>q</italic>, which differentiates it from the Schwarzschild black hole solution. By taking <math altimg='si2.svg'><mi>q</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math>, we compare our results with the Schwarzschild black hole scenario and identify substantial variations. Our research elucidates the impact of the magnetic charge parameter <italic>q</italic> on multiple physical parameters of the black hole and offers a comprehensive comparison with the Schwarzschild black hole solution.

Ibrar Hussain

Studying the enigma of particle dynamics using a new type of regular charged black hole

This article investigates the particle motion properties, and plasma lensing in weak gravitational field around a Dyonic black hole solution in a perfect fluid. We analyze the motion of massive and massless particles by studying the effective potential, energy, and angular momentum as a function of electric and magnetic charge, the fluid parameters, <bold>a</bold>, and the surrounding field parameter <italic>&#969;</italic>. We have examined the features using Dyonic black holes, including horizon structure, photon orbit, and ISCO radius, to better understand the effect of black hole parameters on their behavior. Our findings indicate that by increasing the electric charge <math altimg='si1.svg'><msub><mrow><mi>q</mi></mrow><mrow><mi>E</mi></mrow></msub></math>, magnetic charge, <math altimg='si2.svg'><msub><mrow><mi>q</mi></mrow><mrow><mi>M</mi></mrow></msub></math>, and surrounding field parameter <italic>&#969;</italic> brings the orbit closer to the central compact object. In contrast, the fluid parameter <bold>a</bold> has an opposing effect, shifting the ISCO outward. Wa have also determined the deflection angle of light rays surrounding the black hole in a weak plasma environment using the uniform and <italic>SIS</italic> plasma fields, and found that black holes parameters have clear effect on deflection angle.

Sikander Mehmood

Wajiha Tanveer

Waleed Ahmad

Awad A. Ibraheem

Rana Muhammad Zulqarnain

Plasma lensing and particle dynamics in the vicinity of a Dyonic black hole solution in the context a perfect fluid

This study tested the geometric structure and dynamic behavior of particles around a non-rotating black hole (BH) featuring a de Sitter core. We derive the space-time metric and analyze key features such as the lapse function, effective potential, innermost stable circular orbits (ISCOs), and particle trajectories. The Hamiltonian framework reveals that the de Sitter core radius <italic>R</italic> significantly influences particle dynamics: a larger <italic>R</italic> shifts the effective potential minima closer to the horizon, enhances the attractive effective force and marginally impacts the ISCO radii. Numerical solutions of motion demonstrate modified trajectories compared to Schwarzschild BHs, with a higher center of mass energy (CME) near the horizon for larger <italic>R</italic>. Harmonic oscillation frequencies, periastron precession, and thermodynamic properties, including temperature, specific heat, and Hawking radiation emission, are quantified. Thermodynamic stability is tested for specific parameter ranges, with the temperature decreasing as <italic>R</italic> increases. Our results explain the relation between the de Sitter core and gravitational dynamics, providing insight into the stability and energy properties.

Badr S. Alkahtani

Epicyclic oscillations, particle collisions, emission energy and thermal fluctuation around a black hole with de-sitter core

This study investigates the geometric structure, particle dynamics, and thermal properties of the non-rotating Frolov black hole. We analyze the black hole geometry and derive the effective potential governing the motion of the test particle, showing the influence of the BH charge <italic>Q</italic> and the parameter <italic>&#945;</italic> on the motion of the particle. Using the Hamiltonian formalism, we determine the angular momentum, energy, and innermost stable circular orbits of the particles, demonstrating that increasing <italic>Q</italic> and <italic>&#945;</italic> shifts the innermost stable circular orbit radii closer to the horizon and reduces the stability of the orbit. The effective force acting on the particles becomes more attractive with higher <italic>Q</italic> and <italic>&#945;</italic>. Harmonic oscillatory motion around stable orbits reveals distinct radial, latitudinal, and axial frequencies, which diminish near the horizon for larger <italic>Q</italic> and <italic>&#945;</italic>. Periastron precession rates similarly decrease with these parameters. The center of mass energy near the horizon escalates with <italic>Q</italic> and <italic>&#945;</italic>, suggesting enhanced energy extraction efficiency. We also study the black hole thermodynamics, and found that the black hole exhibits a positive Hawking temperature and entropy, while the specific heat analysis indicates phase transitions and regions of stability dependent on <italic>Q</italic>, <italic>&#945;</italic>, and the Barrow entropy parameter. The emission energy rates decrease as <italic>Q</italic> and <italic>&#945;</italic> increase. Our results generalize the Schwarzschild black hole case ( <math altimg='si1.svg'><mi>Q</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#945;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math>) and provide critical insights into the interplay between charge, space-time structure, and thermodynamic behavior in Frolov black hole geometries.

S.K. Maurya

Muhammad Aslam

Muhammad Yousaf Malik

Barrow entropy effects on thermodynamics and quasi-periodic oscillations around a Frolov black hole