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

  • Junji Jia
  • Jiawei Liu
  • Xionghui Liu
  • Zhongyou Mo
  • Xiankai Pang
  • Yaoguang Wang
  • Nan Yang
Research Article


The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.


Static spacetime Spherically symmetric spacetime Circular orbit Fixed point 



The work of J. Jia, J. Liu, X. Liu and X. Pang are supported by the NNSF China 11504276 & 11547310, MST China 2014GB109004, Chinese SRFDP 20130141120079 and NSF Hubei ZRY2014000988 /2014CFB695. The work of N. Yang is supported by the NNSF China 31571797 & 31401649.


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Authors and Affiliations

  1. 1.MOE Key Laboratory of Artificial Micro- and Nano-structuresWuhan UniversityWuhanChina
  2. 2.School of Physics and TechnologyWuhan UniversityWuhanChina
  3. 3.Institute of High Energy PhysicsChinese Academy of SciencesBeijingChina
  4. 4.Glyn O. Phillips Hydrocolloid Research CentreHubei University of TechnologyWuhanChina

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