Spinning Test Particles Research Articles

Dragging of the particle spin and spin–spin coupling effect on its periapsis shift

Abstract The periapsis shift (PS) of spinning test particles in the equatorial plane of an arbitrary stationary and axisymmetric spacetime is studied using the post-Newtonian method. The result is expressed as a half-integer power series of $M/p$, where $M$ is the spacetime mass and $p$ is the semilatus rectum. The coefficients of the series are polynomials of the particle spin, the asymptotic expansion coefficients of the metric functions, and the eccentricity of the orbit. The particle spin is shown to have a similar effect as the Lense-Thirring (LT) effect on the PS, and both of them appear from the $(M/p)^{-3/2}$ order in the PS. The coupling between the spacetime and particle spins will increase (or decrease) the PS if they are parallel (or antiparallel). For Jupiter and Saturn rotating around the Sun and exceptionally designed satellites around Mercury and Moon, and the space-based gravitational wave observatories LISA and TaiJi around the Sun, the particle spin effect can be comparable to or even larger than the LT one in size. The PS in other spacetime studied are is not distinguishable from that in the Kerr spacetime to the $(M/p)^{-3/2}$ order.

Spinning particle motion around charged black hole from T-duality

This study examines a spinning particle motion around a charged black hole from T-duality. Initially, our investigation focuses on the lapse function of the metric, revealing that the presence of the black hole’s charge solely induces a shift in the location of the black hole’s horizon. However, with the introduction of l0, we observe the emergence of the second Cauchy horizon (r−). Additionally, we determine the maximum values of black hole parameters within the T-duality framework, guided by the criterion for the existence of the black hole horizon. We employ the Mathisson-Papapetrous-Dixon (MPD) equation to analyze the dynamics of the spinning test particles. Our exploration delves into the influence of the particle’s spin and associated parameters Q and l0 on the effective potential. Subsequently, we investigate the innermost stable circular orbit (ISCO) to establish relationships between the particle’s energy, angular momentum at ISCO, ISCO radius, and the particle’s spin, along with black hole parameters from T-duality. We also focus on superluminal motion, a crucial characteristic distinguishing time-like particles from space-like ones. Numerical values for the particle’s critical spin (smax) necessary to maintain time-like behavior are determined. Finally, we address the collision of spinning particles in the proximity of a compact object. Within this context, we endeavor to identify critical values of the particle’s angular momentum, permitting particles to approach the compact object closely.

Circular motion and collisions of spinning test particles around Kerr–Kiselev black holes

Exploring the effect of exotic fields around black holes on particle dynamics may help to understand the nature of dark matter and energy. The quintessential field can be treated as one of such fields. In this work, we investigate the motion of spinning particles in the vicinity of rotating black holes immersed in quintessential dark energy, characterized by the equation of state (EoS) parameter ω∈(−1;−1/3) governing the equation of state of the dark energy and dimensionless quintessential field parameter C. Using the Mathisson–Papapetrou–Dixon (MPD) equations, we derive the effective potential and study superluminal bound values for the particle spin. Also, we investigate the behaviors of the innermost and outermost stable circular orbit (ISCO & OSCO) of spinning test particles and their energy and angular momentum at the orbits. Note that the OSCO exists due to the third cosmological-like horizon caused by the quintessential field and shows that the ISCO and OSCO coincide at critical values of the quintessential field and EoS parameters, which also depend on the particle and black hole spin. Finally, we explore collisions of spinning particles and analyze the center-of-mass energies and critical angular momentum, which allows the collisions of the particles near the black hole.

Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects.

Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions.

The Ricci Rotation Coefficients in the Description of Trajectories of Spinning Test Particles Off-equatorial Plane in the Gravitational Field of a Rotating Source

We describe the trajectories of circular orbits of spinless and spinning test particles around a rotating body in equatorial and non-equatorial planes via the Mathisson-Papapetrou-Dixon equations. In this paper, these equations include the Ricci rotation coefficients with the purpose of describing not only the curvature of space time, but also the rotation of the spinning test particles that orbit around a rotating massive body. We found a numerical difference between the trajectories of spinless test particles and spinning test particles in the order of 10-7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{10}}^{\\varvec{-7}}$$\\end{document}. We take as parameters: radius, energy, Carter’s constant and angular momentum.

Charged spinning and magnetized test particles orbiting quantum improved charged black holes

In the present work, we aimed to investigate the dynamics of spinning charged and magnetized test particles around both electrically and magnetically charged quantum-improved black holes. We derive the equations of motion for charged spinning test particles using the Mathisson-Papapetrou-Dixon ***equations with the Lorentz coupling term. The radius of innermost stable circular orbits (ISCOs), specific angular momentum, and energy for charged spinless, uncharged spinning, and charged spinning test particles around the charged and non-charged quantum-improved black holes are analyzed separately. We found that the quantum parameter increases the maximum spin value, smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}, which leads to the nonphysical motion (superluminal motion) of the charged spinning test particle. In contrast, the black hole charge decreases its value. We also found that, in contrast to the Reissner Nordström black hole, spinning charged test particles in the quantum-improved charged black hole have higher smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}; moreover, positively charged spinning particles can have higher values of smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document} near the extreme black hole cases when compared with uncharged spinning particles. Finally, we investigate the magnetized test particle’s dynamics in the spacetime of a quantum-improved magnetically charged black hole in Quantum Einstein Gravity using the Hamilton–Jacobi equation. We show that the presence of 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} increases the maximum value of the effective potential and decreases the minimum energy and angular momentum of magnetized particles at their circular orbits. We found an upper constraint in the black hole charge at the ISCO.

Dynamics of spinning test particles around the Kerr–Newman–NUT black hole with quintessence in the Rastall gravity

Dynamics of spinning test particles around the Kerr–Newman–NUT black hole with quintessence in the Rastall gravity

Chaotic motion and Periastron precession of spinning test particles moving in the vicinage of a Schwarzschild black hole surrounded by a quintessence matter field

Chaotic motion and Periastron precession of spinning test particles moving in the vicinage of a Schwarzschild black hole surrounded by a quintessence matter field

Equatorial orbits of spinning test particles in rotating boson stars

In this paper, we study circular orbits of spinning test particles in the background of a rotating boson star. Using the pole-dipole approximation and neglecting the back-reaction of the spinning test particle on the spacetime, the equation of motion of the spinning test particle is described by the Mathisson–Papapetrou–Dixon equation. We solve this equation under the Tulczyjew spin-supplementary condition and obtain the four-momentum and four-velocity of the spinning test particle. Quite different from the spinless particle, the effective potential of the spinning particle with zero orbital angular momentum goes to infinite at the center of the rotating boson star. This will lead to the fact that the spinning particle can not pass through the center of the boson star. However, when the spin angular momentum and orbital angular momentum satisfy 2{bar{s}}+{bar{l}}=0, the effective potential is not divergent anymore and the spinning particle can pass through the center of the rotating boson star. We still investigate how the spin affects the structure of the circular orbits and we find that the spin will induce the larger or smaller regions of no circular orbits, unstable circular orbits, and stable circular orbits. Moreover, the radius and energy of the circular orbit will be decreased or increased by the particle spin. These results will have an important application in testing the gravitational waves in the boson star background.

Motion of a spinning particle around an improved rotating black hole

Using the Mathisson–Papapetrou–Dixon equations together with the Tulczyjew spin-supplementary condition, we study the circular orbits of a spinning test particle moving in the equatorial plane of a quantum improved Rotating Black Hole (RBH) spacetime. This background metric incorporates a position-dependent gravitational constant [Formula: see text] and its behavior determines the quantum corrections to the properties of the Innermost Stable Circular Orbit (ISCO). The obtained results show that the radius of the event horizon as well as the radius of the ISCO for the quantum improved RBH are smaller than those of the Schwarzschild or Kerr solutions.

Spinning test particle motion around a rotating wormhole

In this work, we investigated the motion of spinning test particles around a rotating wormhole, extending, in this way, the previous work of Benavides-Gallego et al. [Phys. Rev. D 101, 124024 (2020)] to the general case. Using the Mathisson-Papapetrou-Dixon equations, we study the effective potential, circular orbits, and the innermost stable circular orbit (ISCO) of spinning test particles. We found that both the particle and wormhole spins affect the location of the ISCO significantly. On the other hand, similar to the nonrotating case, we also found two possible configurations in the effective potential: plus and minus. Furthermore, the minimum value of the effective potential is not at the throat due to its spin $a$, in contrast to the motion of the nonspinning test particles in a nonrotating wormhole, where the effective potential is symmetric, and its minimum value is at the throat of the wormhole. In the case of the ISCO, we found that it increases as the spin of the wormhole $a$ increases, in contrast to black holes where the presence of spin decreases the value of the ISCO. Finally, since the dynamical four-momentum and kinematical four-velocity of the spinning particle are not always parallel, we consider the superluminal bound, finding that the allowed values of the dimensionless particle's spin $s$ change as the wormhole's spin $a$ increases.

Motion of charged and spinning particles influenced by dark matter field surrounding a charged dyonic black hole

We investigate the motion of massive charged and spinning test particles around a charged dyonic black hole spacetime surrounded by perfect fluid scalar dark matter field. We obtain the equations of motion and find the expressions for the four-velocity for the case of a charged particle, and four-momentum components for the case of a spinning particle. The trajectories for various values of electric $Q_{e}$ and magnetic $Q_{m}$ charges are investigated under the influence of dark matter field $\lambda$. We find the equations of motion of a spinning particle that follows a non-geodesic trajectory via Lagrangian approach in addition to the charged and non-spinning particles that follow geodesic motion in this set-up. We study in detail the properties of innermost stable circular orbits (ISCOs) in the equatorial plane. The study of ISCOs of a spinning massive particle is done by using the pole-dipole approximation. We show that, in addition to the particle's spin, the dark matter field parameter $\lambda$ and black hole charges ($Q_{m}\;\text{and}\;Q_{e}$) have a significant influence on the ISCOs of spinning particles. It is observed that if the spin is parallel to the total angular momentum $J$ (i.e. $\mathcal{S}>0$), the ISCO parameters (i.e.$r_{ISCO}, L_{ISCO}\;\text{and}\; E_{ISCO}$) of a spinning particle are smaller than those of a non-spinning particle, whereas if the spin is anti-parallel to total angular momentum $J$ (i.e. $\mathcal{S}<0$), the value of the ISCO parameters is greater than that of the non-spinning particle. We also show that for the corresponding values of spin parameter S, the behaviour of Keplerian angular frequency of ISCO $\Omega_{ISCO}$ is opposite to that of $r_{ISCO}, L_{ISCO}\; \text{and}\; E_{ISCO}$.

Motion of spinning particles around electrically charged black hole in Eddington-inspired Born–Infeld gravity

A test particle possessing spin angular momentum moves along a non-geodesic path due to an additional spin-curvature force. We study the spinning test particle moving in the vicinity of the electrically charged black hole formation in Eddington-inspired Born–Infeld (EiBI) gravity. Through the numerical analysis of its effective potential and orbits, it is found that the orbital eccentricity reduces as the deviation parameter kappa increases. By comparing the orbits for the observed stars around Sagittarius A*, we conclude that the observed orbits with too large radii can not give a stringent constraint with acceptable magnitude. To dig out the potential observation effects of the relations between the orbits and parameter kappa , we mainly focus on the orbits in the vicinity of black hole in this paper. The parameters of inner most stable circular orbit (ISCO) decrease monotonously with kappa when the spin angular momentum is small, however they change non-monotonously with kappa when the spin is large enough. Moreover, the spin dependences of ISCO parameters have similar behavior to that of Reissner–Nordström (RN) black hole. We analyze the causality of the circular orbits by using the superluminal constraint condition as well. As a result, two new parameter regions may emerge in case of large kappa , where the particle has two stable circular orbits with one subluminal and the other superluminal.

Epicyclic oscillations in spinning particle motion around Kerr black hole applied in models fitting the quasi-periodic oscillations observed in microquasars and AGNs

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries or quasars can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus fit the data of QPOs observed in the well known microquasars as well as active galactic nuclei (AGNs) in the framework of the model of geodesic oscillations of Keplerian disks modified for the epicyclic oscillations of spinning test particles orbiting Kerr BHs. We show that the modified geodesic models of QPOs can explain the observational fixed data from the microquasars and AGNs but not for all sources. We perform a successful fitting of the high frequency QPOs models of epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, and discuss the corresponding constraints of parameters of the model, which are the spin of the test particle, mass and rotation of the BH.

Motion of Charged Spinning Particles in a Unified Field

Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in a gravitational field. The new method used for derivation, the Bazanski method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.

Spinning test particle motion around a traversable wormhole

The motion of spinning test particles around a traversable wormhole is investigated using the Mathisson Papapetrous Dixon equations, which couple the Riemann tensor with the antisymmetric tensor $S^{ab}$, related to the spin of the particle. Hence, we study the effective potential, circular orbits, and innermost stable circular orbit ISCO of spinning particles. We found that the spin affects significantly the location of the ISCO, in contrast with the motion of nonspinning particles, where the ISCO is the same in both the upper and lower universes. On the other hand, since the dynamical fourmomentum and kinematical fourvelocity of the spinning particle are not always parallel, we also consider a superluminal bound on the particles motion. In the case of circular orbits at the ISCO, we found that the motion of particles with an adimensional spin parameter lower greater than $s=-1.5$ $(1.5)$ is forbidden. The spin interaction becomes important for Kerr black hole orbiting super massive wormholes SMWH.

Confinement of bosonic and spinning particles in braneworlds

In this paper the confinement of bosonic and spinning test particles in smooth Randall-Sundrum models is studied. For this, we show the possibility of finding an effective potential that describes the motion of the particle over the extra dimension. For the bosonic case, it is a known fact that free test particles can be located neither on thin nor on thick branes. Recently, a coupling to a scalar field has been used to localize a limited range of masses. Up to now, no trapped test particles of any mass over the brane were found. In order to solve this, it is shown that a coupling with the dilaton may trap particles of any mass. Next, the spinning particle is analyzed. The spin variables, , introduced an interaction with the Riemann curvature tensor. It introduced a correction to the effective potential. By analyzing it, it was found that the spinning particle may be localized at a different position from the one of the brane. It is also shown that a spinning particle over the brane may escape to infinity. Therefore, it is concluded that free bosonic and spinning particles are not trapped in the brane.

Circular motion and the innermost stable circular orbit for spinning particles around a charged Hayward black hole background

The circular orbits of a spinning test particle moving around a charged Hayward black hole is investigated by using the Mathisson–Papapetrou–Dixon equations together with the Tulczyjew spin-supplementary condition. By writing the equations of motion, the effective potential for the description of the test particle is obtained to study the properties of the Innermost Stable Circular Orbit (ISCO). The results show that the ISCO radii for spinning particles moving in the charged Hayward background differ from those obtained in the corresponding Schwarzschild or Reissner–Nordstrom spacetimes, depending on the values of the electric charge and the length-scale parameter of the metric. When the spin of the particle and its orbital angular momentum are aligned, an increase in the spin produces a decrease in the ISCO radius, while in the case in which the spin of the particle and its orbital angular momentum are anti-aligned, an increase in the spin results in an increase of the radius of the ISCO.

Spinning Test Particle in Four-Dimensional Einstein–Gauss–Bonnet Black Holes

In this paper, we investigate the motion of a classical spinning test particle in a background of a spherically symmetric black hole based on the novel four-dimensional Einstein–Gauss–Bonnet gravity [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)]. We find that the effective potential of a spinning test particle in this background could have two minima when the Gauss–Bonnet coupling parameter α is nearly in a special range −8&lt;α/M2&lt;−2 (M is the mass of the black hole), which means a particle can be in two separate orbits with the same spin-angular momentum and orbital angular momentum, and the accretion disc could have discrete structures. We also investigate the innermost stable circular orbits of the spinning test particle and find that the corresponding radius could be smaller than the cases in general relativity.

Persistent gravitational wave observables: Nonlinear plane wave spacetimes

In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of gravitational radiation. We defined three specific examples of persistent observables: a generalization of geodesic deviation that allowed for arbitrary acceleration, a holonomy observable involving a closed curve, and an observable that can be measured using a spinning test particle. For linearized plane waves, we showed that our observables could be determined just from one, two, and three time integrals of the Riemann tensor along a central worldline, when the observers follow geodesics. In this paper, we compute these three persistent observables in nonlinear plane wave spacetimes, and we find that the fully nonlinear observables contain effects that differ qualitatively from the effects present in the observables at linear order. Many parts of these observables can be determined from two functions, the transverse Jacobi propagators, and their derivatives (for geodesic observers). These functions, at linear order in the spacetime curvature, reduce to the one, two, and three time integrals of the Riemann tensor mentioned above.