Geodesic motions of test particles in a relativistic core–shell spacetime

Liu, Lei; Wu, Xiaoxia; Huang, Guoquan

doi:10.1007/s10714-017-2193-z

Cited by 18 publications

(15 citation statements)

References 58 publications

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“…A projection map on the projection of a vector in extended phase space back to the original phase space is also necessary. Liu et al [52] showed that sequent permutations of coordinates and momenta are a good choice of the mixing maps. Luo et al [53] found that midpoint permutations between coordinates and those between momenta are the best choice of the mixing maps.…”

Section: B Construction Of Symplectic-like Integrators In Extended Ph...mentioning

confidence: 99%

“…( 49) and ( 51), then f SO has 3PN spin-spin coupling and 3.5PN spin-orbit interaction. Thus, besides the terms in the approximate equations (52), many other terms such as the 2.5PN spin-orbit coupling and the 3PN spin-spin contribution are included in the exact equations (53). The 2.5PN spin-orbit and 3PN spin-spin contributions are implicitly hidden in the exact equations, but are absent in the approximate equations.…”

Section: A Dynamical Equationsmentioning

confidence: 99%

“…[49,50]. The extended phase space symplectic-like schemes with optimal mixing maps were applied to PN systems of spinning compact binaries and other inseparable Hamiltonian problems [51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

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Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Pan,

Wu,

Liang

2021

Preprint

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Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy and angular momentum. Doubling the phase-space variables of positions and momenta in the coherent equations, we establish extended phase-space symplectic-like integrators with the midpoint permutations. The velocities should be solved iteratively from the algebraic equations of the momenta defined by the Lagrangian during the course of numerical integrations. It is shown numerically that a fourthorder extended phase-space symplectic-like method exhibits good long-term stable error behavior in energy and angular momentum, as a fourth-order implicit symplectic method with a symmetric composition of three second-order implicit midpoint rules or a fourth-order Gauss-Runge-Kutta implicit symplectic scheme does. For given time step and integration time, the former method is superior to the latter integrators in computational efficiency. The extended phase-space method is used to study the effects of the parameters and initial conditions on the orbital dynamics of the coherent Euler-Lagrange equations for a post-Newtonian circular restricted three-body problem. It is also applied to trace the effects of the initial spin angles, initial separation and initial orbital eccentricity on the dynamics of the coherent post-Newtonian Euler-Lagrange equations of spinning compact binaries.

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Section: B Construction Of Symplectic-like Integrators In Extended Ph...mentioning

confidence: 99%

Section: A Dynamical Equationsmentioning

confidence: 99%

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Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Pan,

Wu,

Liang

2021

Preprint

Self Cite

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“…found that the midpoint permutations between the original coordinates and the extended coordinates and the midpoint permutations between the original momenta and the extended momenta are the best mixing maps. The explicit extended phase space symplectic-like integrators with the midpoint permutations are well applicable to nonconservative nonseparable systems , logarithmic Hamiltonians (Li & Wu 2017), relativistic core-shell spacetimes (Liu et al 2017), and magnetized Ernst-Schwarzschild spacetimes (Li & Wu 2019). Recently, Pan et al (2021) considered the construction of semiexplicit extended phase space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes

Zhou,

Zhang,

Liu

et al. 2022

Preprint

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In recent publications, the construction of explicit symplectic integrators for Schwarzschild and Kerr type spacetimes is based on splitting and composition methods for numerical integrations of Hamiltonians or time-transformed Hamiltonians associated with these spacetimes. Such splittings are not unique but have various choices. A Hamiltonian describing the motion of charged particles around the Schwarzschild black hole with an external magnetic field can be separated into three, four and five explicitly integrable parts. It is shown through numerical tests of regular and chaotic orbits that the three-part splitting method is the best one of the three Hamiltonian splitting methods in accuracy. In the three-part splitting, optimized fourth-order partitioned Runge-Kutta and Runge-Kutta-Nyström explicit symplectic integrators exhibit the best accuracies. In fact, they are several orders of magnitude better than the fourth-order Yoshida algorithms for appropriate time steps. The former algorithms need small additional computational cost compared with the latter ones. Optimized sixth-order partitioned Runge-Kutta and Runge-Kutta-Nyström explicit symplectic integrators have no dramatic advantages over the optimized fourth-order ones in accuracies during long-term integrations due to roundoff errors. The idea finding the integrators with the best performance is also suitable for Hamiltonians or time-transformed Hamiltonians of other curved spacetimes including the Kerr type spacetimes. When the numbers of explicitly integrable splitting sub-Hamiltonians are as small as possible, such splitting Hamiltonian methods would bring better accuracies. In this case, the optimized fourth-order partitioned Runge-Kutta and Runge-Kutta-Nyström methods are worth recommending. Unified Astronomy Thesaurus concepts: Black hole physics (159); Computational methods (1965); Computational astronomy (293); Celestial mechanics (211)

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“…Bearing in mind that the multipole moments represent the intrinsic structure of the source, in the context of general relativity several investigations have been carried out aiming to determine their influence on the geodesic motion of test particles (see e.g., Gair & Mandel 2008;Ramos-Caro et al 2011;Liu et al 2017;Wang et al 2018). In Vieira & Letelier (1996), the dynamic effect of quadrupolar and octupolar moments describing a superimposed halo with a black hole, within the framework of exact solutions in general relativity, has been investigated.…”

Section: Introductionmentioning

confidence: 99%

Effect of Multipole Moments in the Weak Field Limit of a Black Hole Plus Halo Potential

Dubeibe

Saeed

Zotos

2021

ApJ

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In this paper, we consider a Newtonian system whose relativistic counterpart describes a superimposed halo with a black hole. Our aim is to determine how the quadrupole and octupole moments affect the nature of the motion of a test particle, moving in the close vicinity of the black hole. The different types of trajectories for the test particle are mainly classified as bounded, collisional, and escaping, by using modern color-coded basin diagrams. Moreover, an additional analysis is carried out for distinguishing between the different types of bounded motion (regular, sticky, and chaotic). Our results strongly indicate that the multipole moments, along with the total orbital energy, highly affect the final state of the test particle, while at the same time the basin geometry of the phase space tends to be highly dominated by collision and escape orbits.

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Geodesic motions of test particles in a relativistic core–shell spacetime

Cited by 18 publications

References 58 publications

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes

Effect of Multipole Moments in the Weak Field Limit of a Black Hole Plus Halo Potential

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