Radius Of Innermost Stable Circular Orbit Research Articles

Collisions and dynamics of particles with magnetic dipole moment and electric charge near magnetized rotating Kerr black holes

Analysis of test magnetized and charged particles around black holes immersed in external magnetic fields may help to explain the observed astrophysical phenomena related to black holes, such as the acceleration of particles up to high energies. In this sense, we studied the circular motion of test-charged particles with magnetic dipole orbiting around magnetized rotating Kerr black holes. First, we derive the effective potential for the circular motion of such particles, including interactions between the external magnetic field and the electric charge, and the magnetic interaction between the magnetic dipole. In addition, we analyze the angular momentum and energy of particles corresponding to circular orbits. The effects of magnetic interaction and coupling parameters on the position of innermost stable circular orbits (ISCOs), the energy and angular momentum of the particles at ISCO, and the energy efficiency from the Novikov-Thorne accretion disc have been investigated. We also find cases of degeneracy between magnetic dipole interaction and magnetic coupling parameters, giving the same ISCO radius. Finally, we studied various cases of collisions of neutral, magnetized, and electrically charged particles near rotating Kerr black holes in the presence of external magnetic fields. The critical angular momentum of spinning charged particles is found in which the particles can collide. We also analyze the effects of both magnetic interactions on the center-of-mass energy of the colliding particles.

Circular orbits and collisions of particles with magnetic dipole moment near magnetized Kerr black holes in modified gravity

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

Charged Particles Orbiting Charged Black-Bounce Black Holes

The detailed and comprehensive analysis of radiation processes in accretion disks consisting of electrically charged particles around black holes may provide powerful information about the spacetime geometry of the central black hole. We investigate the circular orbits of electrically charged particles around an electrically charged black-bounce Reissner–Nordström (RN) black hole, known as an RN Simpson–Visser (SV) black hole. We also study the profiles of the innermost stable circular orbits (ISCOs), energy, and angular momentum of the particles in their ISCOs, as well as the efficiency of energy release processes in the accretion disk in the Novikov–Thorne model. Finally, we calculate and study the effects of the black-bounce parameter as well as the black-hole charge on the intensity of the radiation of ultrarelativistic charged particles orbiting the charged RN SV black hole along circular orbits and falling into the black hole. It is observed that the black-bounce parameter essentially decreases the ISCO radius, and consequently the energy extraction and intensity of electromagnetic radiation.

Motion of spinning particles around dynamic phantom AdS black holes

This work is devoted to discussing spinning particles’ motion in the surrounding dynamic phantom AdS Black hole (BH) with phantom scalar field k. The primary goal of this research is to differentiate between the effects of electric and magnetic charges on dynamic phantom AdS BH. The study analyzes the dependence of the innermost stable circular orbit (ISCO), responsible for interactions between charged particles and the external magnetic field, and observes the circular orbits of particles revolving around the compact object. It is also observed that as electric and magnetic charges increase, the ISCO radius decreases. Additionally, stability of orbit, Keplerian frequency, and harmonic oscillations of charged particles are also discussed. We also find the condition, electric and magnetic charges of the dynamic phantom AdS BH effect the energy of the center of mass with magnetized, electrically charged, and neutral particles due to the collision. Lastly, we discuss the accretion process and obtain generalized equations for the speed of sound cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c^2_{s}$$\\end{document} sec, 4-velocity u(r), energy density ρ(r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (r)$$\\end{document} and mass (M˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{M}}$$\\end{document}). We also plot these physical parameters against constant values of mass, electric and magnetic charges, and distinct values of state parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} to study the accretion process. We observe that radial velocity and energy density of the fluid remain positive and negative, and the rate of change of mass is increased and decreased for stiff, dust, quintessence, and phantom-like fluid, respectively.

Quasiperiodic oscillations around hairy black holes in Horndeski gravity

Testing gravity theories and their parameters using observations is an important issue in relativistic astrophysics. In this context, we investigate the motion of test particles and their harmonic oscillations in the spacetime of non-rotating hairy black holes (BHs) in Hordeski gravity, together with astrophysical applications of quasiperiodic oscillations (QPOs). We show possible values of upper and lower frequencies of twin-peak QPOs which may occur in the orbits from innermost stable circular orbits to infinity for various values of the Horndeski parameter q in relativistic precession, warped disk models, and three different sub-models of the epicyclic resonant model. We also study the behaviour of the QPO orbits and their position relative to innermost stable circular orbits (ISCOs) with respect to different values of the parameter q. It is obtained that at a critical value of the Horndeski parameter ISCO radius takes 6M which has been in the pure Schwarzschild case. Finally, we obtain mass constraints of the central BH of microquasars GRS 1915+105 and XTE 1550-564 at the GR limit and the possible value of the Horndeski parameter in the frame of the above-mentioned QPO models. The analysis of orbits of twin peak QPOs with the ratio of upper and lower frequencies 3:2, around the BHs in the frame of relativistic precession (RP) and epicyclic resonance (ER4) QPO models have shown that the orbits locate close to the ISCO. It is obtained that the distance between QPO orbits and ISCO is less than the error of the observations.

Accretion onto a static spherically symmetric regular MOG dark compact object

In astrophysics, the process of a massive body acquiring matter is referred to as accretion. The extraction of gravitational energy occurs as a result of the infall. Since it converts gravitational energy into radiation, accretion onto dark compact objects, e.g. black holes, neutron stars, and white dwarfs is an extremely significant process in the astrophysical context. Accretion process is a fruitful way to explore the features of modified gravity (MOG) theories by testing the behavior of their solutions associated with dark compact objects. In this paper, we study the motion of electrically neutral and charged particles moving in around a regular spherically symmetric MOG dark compact object to explore their related innermost stable circular orbit (ISCO) and energy flux. Then, we turn to investigate the accretion of perfect fluid onto the regular spherically symmetric MOG dark compact object. We obtain analytical expressions for four-velocity and proper energy density of the accreting fluid. We see that the MOG parameter increases the ISCO radius of either electrically neutral or charged test particles while it decreases the corresponding energy flux. Moreover, the energy density and the radial component of the four-velocity of the infalling fluid decrease by increasing the MOG parameter near the central source.

Magnetized Particles with Electric Charge around Schwarzschild Black Holes in External Magnetic Fields

We investigate the dynamics of test particles endowed with both electric charge and a magnetic dipole moment around a Schwarzschild black hole (BH) immersed in an externally asymptotically uniform magnetic field. We further analyse the effective potential and specific angular momentum and energy of the particles. Furthermore, we show that the upper limit for magnetic interaction parameter β increases with increasing cyclotron frequency ωB, while the radius of the innermost stable circular orbit (ISCO) for charged test particles decreases for the upper value of β=βupper. Furthermore, we show that the energy efficiency released from the BH increases up to about 90% due to the presence of the magnetic dipole moment of the test particle. We explore a degeneracy between the spin parameter of rotating Kerr BH and the magnetic parameter for the values of the ISCO radius and energy efficiency. We study in detail the centre of mass energy for collisions of charged and magnetized particles in the environment surrounding the Schwarzchild BH. Finally, as an astrophysical application, we explore the magnetized parameter and cyclotron frequency numerically for a rotating magnetized neutron star. Interestingly, we show that the corresponding values of the above-mentioned parameters for the magnetar PSR J1745-2900 that orbits around the supermassive black hole (SMBH) that exists at the centre of the Milky Way galaxy are ωB≃5 and β≃0.67, respectively, for the magnetic field is about 10 G.

Geodesic motions near an improved Schwarzschild black hole

In this paper, we studied the geodesics of timelike and null like particles near an improved Schwarzschild black hole. The lapse function has been plotted and was found that only one horizon is possible. The equation of motion and effective potential of test particle have been calculated. This equation has an importance in studying the radial free fall and in studying the stability of radial orbits (trajectories). The energy and angular momentum have also been calculated to analysis the cicrular motion and stability of circular orbits. Moreover, Innermost stable circular orbit radius has determined. To get a deeper insight of the nature of these trajectories, we have studied the timelike and null geodesics with the help of the dynamical systems approach. This analysis help us to determine the stability as well as fixed point of phase space trajectories.

Innermost stable circular orbit of spinning particles around a rotating black hole surrounded by perfect fluid dark matter

In this paper, we investigate the innermost stable circular orbit (ISCO) of spinning particles around a rotating black hole surrounded by the perfect fluid dark matter (PFDM). The motion of spinning particles is derived by Mathisson–Papapetrou–Dixon equation and the ISCO parameters are obtained by the radial effective potential. The effect of PFDM density parameter on the motion of spinning particles is analyzed. The results show that the effect of PFDM is nonlinear, and the radius of ISCO varies nonmonotonically with PFDM density parameter.

Electromagnetic Fields around Black Holes in Einstein Æther Gravity

Axial symmetry and stationary properties of spacetime allow to find exact analytical solutions of differential equations describing fields and particles in a gravitational background. The present work is mainly devoted to derivation of exact solutions of Maxwell’s equations for magnetic fields generated by current loops around static black holes (BHs) in Einstein-aether gravity based on the spacetime symmetries in both regions: (i) interior and (ii) exterior to the current loop for a proper observer. The spacetime symmetries are applied in separating variables to solve the second order ordinary differential equation for vector potential of electromagnetic field and the equations of motion of test particles around the aether BH. We also study effects of the aether field on innermost stable circular orbits (ISCOs) of the test particles assuming the current loop position is placed there. It is obtained that the ISCO radius, as well as dipole magnetic moment of the current loop decrease with the increase of the aether parameter c14. Moreover, the performed analysis indicates that the aether field causes a decrease in the magnetic field inside and outside the current loop due to the change of its position.

Constraints on the magnetized Ernst black hole spacetime through quasiperiodic oscillations

We study the dynamics of test particles around a magnetized Ernst black hole considering its magnetic field in the environment surrounding the black hole. We show how its magnetic field can influence the dynamics of particles and epicyclic motion around the black hole. Based on the analysis, we find that the radius of the innermost stable circular orbit (ISCO) for both neutral and charged test particles and epicyclic frequencies are strongly affected by the influence of the magnetic field. We also show that the ISCO radius of charged particles decreases rapidly. It turns out that the gravitational and Lorentz forces of the magnetic field are combined, thus strongly shrinking the values of the ISCO of charged test particles. Finally, we obtain the generic form for the epicyclic frequencies and select three microquasars with known astrophysical quasiperiodic oscillation (QPO) data to constrain the magnetic field. We show that the magnetic field is of the order of magnitude Bsim 10^{-7} Gauss, taking into account the motion of neutral particles in circular orbit about the black hole.

Quasiperiodic oscillations from noncommutative inspired black holes

We investigate the dynamics of test particles in the spacetime of noncommutative inspired black holes (NCi BHs). In this context, we first analyse spacetime properties of the NCi BHs together with innermost stable circular orbits (ISCOs) for the particles. It is observed that whereas the ISCO radius does not depend on the NC parameter, the frequencies of the Keplerian orbits and harmonic oscillations are NC parameter dependent. As an application, we consider quasiperiodic oscillations (QPOs) to test effects of the NC gravity around the BHs using twin-peak QPOs frequencies. It is found that the frequency changes even in the presence of the critical NC parameter are smaller than the error in the frequency measurements. The method developed for testing gravity using data from twin peak QPOs may also be applied to other alternate theories of gravity to obtain restrictions on the central BH parameters. We show that the orbits of QPOs lie near ISCO. This assumption may be helpful in solving the ISCO measurement problems in astrophysical observations. In addition, we determine the mass of the central BH in microquasar GRS 1915-105 and the QPO orbit in both the relativistic precession and warped disk models. It is shown that these parameters do not depend on the quantum corrections in the NC gravity. Lastly, we investigate the gravitational capture cross-section for photons and show that the effect of the NC parameter is also less than the error in shadow measurements of the supermassive BH (SMBH) Messier 87 (M87).

Effect of perfect fluid dark matter on particle motion around a static black hole immersed in an external magnetic field

We investigate particle and photon motion in the vicinity of a static and spherically symmetric black hole surrounded by perfect fluid dark matter in the presence of an external asymptotically uniform magnetic field. We determine the radius of the innermost stable circular orbit (ISCO) for charged test particles and the radius for unstable circular photon orbits and show that the effect of the presence of dark matter shrinks the values of ISCO and photon sphere radii. Based on the analysis of the ISCO radius we further show that the combined effects of dark matter and magnetic field can mimic the spin of a Kerr black hole up to a/M≈0.75−0.8. Finally, we consider the effect of the presence of dark matter on the center of mass energy of colliding particles in the black hole vicinity. We show that the center of mass energy grows as the value of the dark matter parameter increases. This result, in conjunction with the fact that, in the presence of an external magnetic field, the ISCO radius can become arbitrarily close to the horizon leads to arbitrarily high energy that can be extracted by the collision process, similarly to what is observed in the super-spinning Kerr case.

Bound orbits around modified Hayward black holes

The neutral time-like particle’s bound orbits around modified Hayward black holes have been investigated. We find that both in the marginally bound orbits (MBO) and the innermost stable circular orbits (ISCO), the test particle’s radius and its angular momentum are all more sensitive to one of the parameters [Formula: see text]. Especially, modified Hayward black holes with [Formula: see text] could mimic the same ISCO radius around the Kerr black hole with the spin parameter up to [Formula: see text]. Small [Formula: see text] could mimic the ISCO of small-spinning test particles around Schwarzschild black holes. Meanwhile, rational (periodic) orbits around modified Hayward black holes have also been studied. The epicyclic frequencies of the quasi-circular motion around modified Hayward black holes are calculated and discussed with respect to the observed Quasi-periodic oscillations (QPOs) frequencies. Our results show that rational orbits around modified Hayward black holes have different values of the energy from the ones of Schwarzschild black holes. The epicyclic frequencies in modified Hayward black holes have different frequencies from Schwarzschild and Kerr ones. These might provide hints for distinguishing modified Hayward black holes from Schwarzschild and Kerr ones by using the dynamics of time-like particles around the strong gravitational field.

Distinguishing regular and singular black holes in modified gravity

This paper is devoted to investigate the possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin peak quasiperiodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The presence of MOG field causes to sufficiently the mpeak in effective potential for a radial motion of test particles. The effect of MOG parameter on specific angular momentum and energy has also studied. As a main part of the paper, we focus on investigations of QPOs around SMOG and RMOG BHs in RP model and the relations of upper and lower frequencies of twin peak QPOs in SMOG and RMOG BH models together with extreme rotating Kerr and Schwarzschild BH. Moreover, possible parameters for the central BHs of the objects GRS J1915 + 105 and XTE 1550 – 564 have also obtained numerically in the relativistic precession (RP) model. Finally, we provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place and show that QPOs can not be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits.

Dynamics of Test Particles and Twin Peaks QPOs around Regular Black Holes in Modified Gravity

In this work, we have presented a detailed analysis of the event horizon of regular black holes (BHs) in modified gravity known as MOG, the so-called regular MOG BH. The motion of neutral particles around the BH has also been explored. The test particle motion study shows that the positive (negative) values of the MOG parameter mimic the spin of a rotating Kerr BH, providing the same values for the innermost stable pro-grade (retrograde) orbits of the particles in the range of the spin parameter a/M∈(−0.4125,0.6946). The efficiency of energy release from the accretion disk by the Novikov–Thorne model has been calculated, and the efficiency was shown to be linearly proportional to the increase of the MOG parameter α. Moreover, we have developed a new methodology to test gravity theories in strong-field regimes using precision data from twin-peaked quasiperiodic oscillations (QPOs) of objects calculating possible values of upper and lower frequencies. However, it is obtained that the positive MOG parameter can not mimic the spin of Kerr BHs in terms of the same QPO frequencies. We have provided possible ranges for upper and lower frequencies of twin-peak QPOs with the ratio of the upper and lower frequencies of 3:2 around regular MOG BHs in the different models. Moreover, as an example, we provide detailed numerical analysis of the QPO of GRS 1915+105 with the frequencies νU=168±5Hz and νL=113±3Hz. It is shown that the central BH of the QPO object can be a regular MOG BH when the value of the parameter is α=0.2844−0.1317+0.0074 and shines in the orbits located at the distance r/M=7.6322−0.0826+0.0768 from the central BH. It is also shown that the orbits where QPOs shine are located near the innermost stable circular orbit (ISCO) of the test particle. The correlation between the radii of ISCO and the QPO orbits is found, and it can be used as a new theoretical way to determine ISCO radius through observational data from the QPOs around various compact objects.

Regular Bardeen Black Holes in Anti-de Sitter Spacetime versus Kerr Black Holes through Particle Dynamics

In this work, test particle dynamics around a static regular Bardeen black hole (BH) in Anti-de Sitter spacetime has been studied. It has been shown for neutral test particles that parameters of a regular Bardeen black hole in Anti-de Sitter spacetime can mimic the rotation parameter of the Kerr metric up to the value a≈0.9 providing the same innermost stable circular orbit (ISCO) radius. We have also explored the dynamics of magnetized particles with a magnetic dipole moment around a magnetically charged regular Bardeen black hole in Anti-de Sitter spacetime. As a realistic astrophysical scenario of the study, we have treated neutron stars orbiting a supermassive black hole (SMBH), in particular, the magnetar PSR J1745-2900 orbiting Sgr A* with the parameter β=10.2, as magnetized test particles. The magnetized particles dynamics shows that the parameter β, negative values of cosmological constant and magnetic charge parameter of the central BH cause a decrease in the ISCO radius. We have compared the effects of the magnetic charge of the Bardeen BH with the spin of rotating Kerr BH and shown that magnetic charge parameter can mimic the spin in the range a/M≃(0,0.7896) when Λ=0 at the range of its values g/M≃(0,0.648).

Particle Motion and Plasma Effects on Gravitational Weak Lensing in Lorentzian Wormhole Spacetime

Here we study particle motion in the specific Lorentzian wormhole spacetime characterized, in addition to the total mass M, with the dimensionless parameter λ. In particular we calculate the radius of the innermost stable circular orbit (ISCO) for test particles and the photonsphere for massless particles. We show that the effect of the dimensionless wormhole parameter decreases the ISCO radius and the radius of the photon orbit. Then, we study plasma effects on gravitational weak lensing in wormhole spacetime and obtain the deflection angle of the light. We show that the effect of λ decreases the deflection angle. We study the effects of uniform and non-uniform plasma on the light deflection angle separately, and show that the uniform plasma causes the deflection angle to be smaller in contrast to the non-uniform plasma.

Charged particle motion around a magnetized Reissner-Nordström black hole

We investigate the dynamics of neutral and charged test particles around axially symmetric magnetized black hole spacetime. We consider its electromagnetic field in the black hole vicinity and study its impact on the dynamics of test particles. We determine the radius of the innermost stable circular orbit (ISCO) for neutral and charged test particles and show that the combined effect of black hole electric charge and magnetic field strongly affects the ISCO radius, thus shrinking its values. We also show that the ISCO radius of positively (negatively) charged particle initially gets increased (decreased) and then gets radically altered with an increase in the value of both black hole electric charge and test particle charge. It turns out that the repulsive (attractive) Coulomb force dominates over the Lorentz force arising from the black hole magnetic field. Typically, black hole rotation causes axially symmetric spacetime case. Similarly, it turns out that a magnetized black hole solution also causes axially symmetric spacetime as a consequence of the presence of magnetic field. We study a degeneracy for the value of the ISCO between the Kerr and the magnetized Reissner-Nordstr\"om black hole geometries and show that the combined effects of black hole charge and magnetic field can be mimicked by Kerr spacetime with the spin parameter up to $a/M\ensuremath{\approx}0.8$. Finally, we consider the center of mass energy of colliding particles and show that an increase in the values of black hole magnetic field and electric charge leads to high center of mass energy extracted by collision of two particles.

Geodesic motion around hairy black holes

In a recent paper Ovalle et al. (2021) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time-like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.