Existence and stability of circular orbits in general static and spherically symmetric spacetimes

Jia, J.; Liu, Jiawei; Liu, Xionghui; Zhongyou, Mo,; Pang, Xiankai; Wang, Yaoguang; Yang, Nan

doi:10.1007/s10714-017-2337-1

Cited by 3 publications

(3 citation statements)

References 33 publications

(39 reference statements)

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“…where ± r and ± θ are two signs introduced when taking the square roots in Eqs. (13) and (14). The motion equations for r and θ coordinates then are found using…”

Section: A Preliminariesmentioning

confidence: 99%

“…The simplest scenario of signal deflection and GL is those of light rays in static and spherically symmetric (SSS) spacetime, or in the equatorial plane of stationary and axisymmetric (SAS) spacetimes in the weak deflection limit (WDL). With the fast developments of astroparticle physics [8,9], gravitational wave detection [10] and black hole (BH) imaging [11,12] however, enormous effort has been devoted to the extension to the deflection and GL of timelike signals [13,14], with finite source and detector distance [15], and in the strong deflection limit [16][17][18]. Different analytical methods were also developed, including the perturbative methods [18][19][20][21] and the more recent Gauss-Bonnet theorem-based methods [22].…”

Section: Introductionmentioning

confidence: 99%

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Institute of International Law Wuhan University

Yushkov¹

2020

China & WTO Rev.

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In this work, we develop a general perturbative procedure to find the off-equatorial plane deflections in the weak deflection limit in general stationary and axisymmetric spacetimes satisfying some common variable separation conditions. Deflections of both null and timelike rays with the finite distance effect of the source and detector taken into account are obtained as dual series of M/r0 and r0/r s,d . These deflections allow a set of exact gravitational lensing equations from which the images' apparent angular positions are solved. The method and general results are then applied to the Kerr-Newmann, Kerr-Sen, and rotating Simpson-Visser spacetimes to study the effect of the spin and characteristic (effective) charge of the spacetimes and the source altitude on the deflection angles and image apparent angles. It is found that in general, both the spacetime spin and charge only affect the deflections from the second non-trivial order, while the source altitude influences the deflection from the leading order. Because of these, it is found that in gravitational lensing in realistic situations, it is hard to measure the effects of the spacetime spin and charge from the images' apparent locations. We also presented the off-equatorial deflections in the rotating Bardeen, Hayward, Ghosh, and Tinchev black hole spacetimes.

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“…where ± r and ± θ are two signs introduced when taking the square roots in Eqs. (13) and (14). The motion equations for r and θ coordinates then are found using…”

Section: A Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Institute of International Law Wuhan University

Yushkov¹

2020

China & WTO Rev.

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“…(We avoid the use of the term "marginally stable orbits". See [8], [9] and [10]. The orbits are also referred to as "indifferently stable".…”

Section: And Below)mentioning

confidence: 99%

Boundary Orbits: 1 Static Spacetimes

Nasereldin,

Lake

2019

Preprint

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The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static spherically symmetric case, it is well known that the introduction of a cosmological constant in vacuum leads to the study of quartic polynomials in order to locate boundary orbits, those that straddle between stable and unstable orbits. These orbits are often referred to as "marginally stable orbits" or "indifferently stable orbits". A comprehensive study of texts offers little clarification as to the stability or instability of these boundary orbits. Here we argue that the direct use of second order perturbation theory immediately shows that these boundary orbits are unstable in the perturbative sense. Our study here includes the two-particle Curzon-Chazy solution.

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Existence and stability of circular orbits in static and axisymmetric spacetimes

Jia¹,

Pang²,

Yang³

2018

Gen Relativ Gravit

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The existence and stability of timelike and null circular orbits (COs) in the equatorial plane of general static and axisymmetric (SAS) spacetime are investigated in this work. Using the fixed point approach, we first obtained a necessary and sufficient condition for the non-existence of timelike COs. It is then proven that there will always exist timelike COs at large ρ in an asymptotically flat SAS spacetime with a positive ADM mass and moreover, these timelike COs are stable. Some other sufficient conditions on the stability of timelike COs are also solved. We then found the necessary and sufficient condition on the existence of null COs. It is generally shown that the existence of timelike COs in SAS spacetime does not imply the existence of null COs, and vice-versa, regardless whether the spacetime is asymptotically flat or the ADM mass is positive or not. These results are then used to show the existence of timelike COs and their stability in an SAS Einstein-Yang-Mills-Dilaton spacetimes whose metric is not completely known. We also used the theorems to deduce the existence of timelike and null COs in some known SAS spacetimes.

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Existence and stability of circular orbits in general static and spherically symmetric spacetimes

Cited by 3 publications

References 33 publications

Institute of International Law Wuhan University

Institute of International Law Wuhan University

Boundary Orbits: 1 Static Spacetimes

Existence and stability of circular orbits in static and axisymmetric spacetimes

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