Equivalence between two charged black holes in dynamics of orbits outside the event horizons

Zhang, Hongxing; Zhou, Naying; Liu, Wenfang; Wu, Xiaoxia

doi:10.1007/s10714-022-02998-1

Cited by 15 publications

(12 citation statements)

References 38 publications

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“…Therefore, the accuracies in the energies and solutions with the original coefficients are almost the same as those with the new coefficients. That is to say, the numerical results should be correct for the original coefficients used in the published article and in Yang et al (2022) and Zhang et al (2022). In spite of this, the new coefficients in the double-precision environment should be recommended in the published article, in Wu et al (2022), Yang et al (2022), andZhang et al (2022), and in future works.…”

Section: Correct Coefficients Of the Optimal Explicit Symplectic Prk ...mentioning

confidence: 99%

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

Zhou

Zhang

Liu

et al. 2022

ApJ

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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 options. 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 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 first two algorithms have a 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 accuracy during long-term integrations due to roundoff errors. The idea of finding the integrators with the best performance is also suitable for Hamiltonians or time-transformed Hamiltonians of other curved spacetimes including 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.

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Section: Correct Coefficients Of the Optimal Explicit Symplectic Prk ...mentioning

confidence: 99%

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

Zhou

Zhang

Liu

et al. 2022

ApJ

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“…Hamiltonians for some other curved spacetimes such as the Kerr metric are not directly split into Equation (1). However, their time-transformed Hamiltonians have the splitting form of Equation (1), as was claimed by several authors (Wu et al 2021;Sun et al 2021aSun et al , 2021bZhang et al , 2022. In what follows, two such types of curved spacetimes are given.…”

Section: Indirect Splitting Methods In Two Types Of Curved Spacetimesmentioning

confidence: 60%

“…The three-part split is what we want. Zhang et al (2022) gave a similar splitting to another regular black hole metric.…”

Section: Regular Black Holesmentioning

confidence: 69%

Explicit Symplectic Methods in Black Hole Spacetimes

Wang

Sun

et al. 2022

ApJ

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Many Hamiltonian problems in the solar system are separable into two analytically solvable parts, and thus serve as a great chance to develop and apply explicit symplectic integrators based on operator splitting and composing. However, such constructions are not in general available for curved spacetimes in general relativity and modified theories of gravity because these curved spacetimes correspond to nonseparable Hamiltonians without the two-part splits. Recently, several black hole spacetimes such as the Schwarzschild black hole were found to allow for the construction of explicit symplectic integrators, since their corresponding Hamiltonians are separable into more than two explicitly integrable pieces. Although some other curved spacetimes including the Kerr black hole do not have such multipart splits, their corresponding appropriate time-transformation Hamiltonians do. In fact, the key problem in obtaining symplectic analytically integrable decomposition algorithms is how to split these Hamiltonians or time-transformation Hamiltonians. Considering this idea, we develop explicit symplectic schemes in curved spacetimes. We introduce a class of spacetimes whose Hamiltonians are directly split into several explicitly integrable terms. For example, the Hamiltonian of a rotating black ring has a 13-part split. We also present two sets of spacetimes whose appropriate time-transformation Hamiltonians have the desirable splits. For instance, an eight-part split exists in a time-transformed Hamiltonian of a Kerr–Newman solution with a disformal parameter. In this way, the proposed symplectic splitting methods can be used widely for long-term integrations of orbits in most curved spacetimes we know of.

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“…In the framework of GR, the Schwarzschild or Kerr metric describes the space-time of an uncharged BH. However, in modified and alternative theories of gravity, there are other possible solutions for the description of the space-time of BHs [26][27][28][29][30][31]. The predictions of different theories of gravity are different, so a universal and reasonable theory about the GWs of an X-MRI should be model-independent.…”

Section: Krz Prametrized Metricmentioning

confidence: 99%

Measurement of the Central Galactic Black Hole by Extremely Large Mass-Ratio Inspirals

et al. 2022

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In the galaxy, extremely large mass-ratio inspirals (X-MRIs) composed of brown dwarfs and the massive black hole at the galactic center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty X-MRI systems by an axisymmetric Konoplya–Rezzolla–Zhidenko metric with varied parameters. We find that the mass, spin, and deviation parameters of the Kerr black hole can be determined accurately (∼10−5−10−6) with only one X-MRI event with a high signal-to-noise ratio. The measurement of the above parameters could be improved with more X-MRI observations.

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Equivalence between two charged black holes in dynamics of orbits outside the event horizons

Cited by 15 publications

References 38 publications

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

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

Explicit Symplectic Methods in Black Hole Spacetimes

Measurement of the Central Galactic Black Hole by Extremely Large Mass-Ratio Inspirals

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