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Gauge invariant perturbations of general spherically symmetric spacetimes

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Abstract

In this paper, the gauge choices in general spherically symmetric spacetimes are explored. In particular, we construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge, respectively. The particular cases for l = 0,1 are also investigated. Our results provide analytical calculations of metric perturbations in general spherically symmetric spacetimes, which can be applied to various cases, including the effective-one-body problem. A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.

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References

  1. T. Regge, and J. A. Wheeler, Phys. Rev. 108, 1063 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  2. L. A. Edelstein, and C. V. Vishveshwara, Phys. Rev. D 1, 3514 (1970).

    Article  ADS  Google Scholar 

  3. F. J. Zerilli, Phys. Rev. Lett. 24, 737 (1970).

    Article  ADS  Google Scholar 

  4. F. J. Zerilli, Phys. Rev. D 2, 2141 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  5. V. Moncrief, Ann. Phys. 88, 323 (1974).

    Article  ADS  Google Scholar 

  6. S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, Oxford, 1992).

    MATH  Google Scholar 

  7. C. V. Vishveshwara, Nature 227, 936 (1970).

    Article  ADS  Google Scholar 

  8. S. Chandrasekhar, and S. L. Detweiler, Proc. R. Soc. Lond. A 344, 441 (1975).

    Article  ADS  Google Scholar 

  9. V. Ferrari, and B. Mashhoon, Phys. Rev. Lett. 52, 1361 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  10. K. D. Kokkotas, and B. G. Schmidt, Living Rev. Relativ. 2, 2 (1999), arXiv: gr-qc/9909058.

    Article  ADS  Google Scholar 

  11. H. P. Nollert, Class. Quantum Grav. 16, R159 (1999).

    Article  MathSciNet  Google Scholar 

  12. V. Cardoso, arXiv: gr-qc/0404093.

  13. E. Berti, V. Cardoso, and A. O. Starinets, Class. Quantum Grav. 26, 163001 (2009).

    Article  ADS  Google Scholar 

  14. P. Pani, Int. J. Mod. Phys. A 28, 1340018 (2013), arXiv: 1305.6759.

    Article  ADS  Google Scholar 

  15. R. A. Konoplya, and A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011), arXiv: 1102.4014.

    Article  ADS  Google Scholar 

  16. M. Davis, R. Ruffini, W. H. Press, and R. H. Price, Phys. Rev. Lett. 27, 1466 (1971).

    Article  ADS  Google Scholar 

  17. K. Martel, Phys. Rev. D 69, 044025 (2004), arXiv: gr-qc/0311017.

    Article  ADS  MathSciNet  Google Scholar 

  18. R. H. Price, Phys. Rev. D 5, 2439 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  19. M. Dafermos, G. Holzegel, and I. Rodnianski, Acta Math. 222, 1 (2019).

    Article  MathSciNet  Google Scholar 

  20. K. Prabhu, and R. M. Wald, Class. Quantum Grav. 35, 235004 (2018), arXiv: 1807.09883.

    Article  ADS  Google Scholar 

  21. V. Moncrief, Ann. Phys. 88, 343 (1974).

    Article  ADS  Google Scholar 

  22. U. H. Gerlach, and U. K. Sengupta, Phys. Rev. D 19, 2268 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  23. U. H. Gerlach, and U. K. Sengupta, Phys. Rev. D 22, 1300 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  24. K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).

    Article  ADS  Google Scholar 

  25. K. Martel, and E. Poisson, Phys. Rev. D 71, 104003 (2005), arXiv: gr-qc/0502028.

    Article  ADS  MathSciNet  Google Scholar 

  26. M. Lenzi, and C. F. Sopuerta, Phys. Rev. D 104, 084053 (2021), arXiv: 2108.08668.

    Article  ADS  Google Scholar 

  27. B. Preston, and E. Poisson, Phys. Rev. D 74, 064010 (2006), arXiv: gr-qc/0606094.

    Article  ADS  MathSciNet  Google Scholar 

  28. J. E. Thompson, H. Chen, and B. F. Whiting, Class. Quantum Grav. 34, 174001 (2017), arXiv: 1611.06214.

    Article  ADS  Google Scholar 

  29. S. L. Detweiler, Phys. Rev. D 77, 124026 (2008), arXiv: 0804.3529.

    Article  ADS  MathSciNet  Google Scholar 

  30. E. Corrigan, and E. Poisson, Class. Quantum Grav. 35, 137001 (2018), arXiv: 1804.00708.

    Article  ADS  Google Scholar 

  31. H. Kodama, and A. Ishibashi, Prog. Theor. Phys. 110, 701 (2003), arXiv: hep-th/0305147.

    Article  ADS  Google Scholar 

  32. A. Ishibashi, and H. Kodama, Prog. Theor. Phys. 110, 901 (2003), arXiv: hep-th/0305185.

    Article  ADS  Google Scholar 

  33. H. Kodama, and A. Ishibashi, Prog. Theor. Phys. 111, 29 (2004), arXiv: hep-th/0308128.

    Article  ADS  Google Scholar 

  34. A. Ishibashi, and H. Kodama, Prog. Theor. Phys. Suppl. 189, 165 (2011), arXiv: 1103.6148.

    Article  ADS  Google Scholar 

  35. T. Takahashi, and J. Soda, Phys. Rev. D 79, 104025 (2009), arXiv: 0902.2921.

    Article  ADS  MathSciNet  Google Scholar 

  36. T. Takahashi, and J. Soda, Prog. Theor. Phys. 124, 911 (2010), arXiv: 1008.1385.

    Article  ADS  Google Scholar 

  37. D. C. Zou, and Y. S. Myung, Phys. Rev. D 101, 084021 (2020), arXiv: 2001.01351.

    Article  ADS  MathSciNet  Google Scholar 

  38. L. Heisenberg, R. Kase, and S. Tsujikawa, Phys. Rev. D 97, 124043 (2018), arXiv: 1804.00535.

    Article  ADS  Google Scholar 

  39. K. Tomikawa, and T. Kobayashi, Phys. Rev. D 103, 084041 (2021), arXiv: 2101.03790.

    Article  ADS  Google Scholar 

  40. A. Buonanno, and T. Damour, Phys. Rev. D 59, 084006 (1999), arXiv: gr-qc/9811091.

    Article  ADS  MathSciNet  Google Scholar 

  41. A. Buonanno, and T. Damour, Phys. Rev. D 62, 064015 (2000), arXiv: gr-qc/0001013.

    Article  ADS  Google Scholar 

  42. J. Jing, S. Chen, M. Sun, X. He, M. Wang, and J. Wang, Sci. China-Phys. Mech. Astron. 65, 260411 (2022), arXiv: 2112.09838.

    Article  ADS  Google Scholar 

  43. E. Berti, K. Yagi, and N. Yunes, Gen. Relativ. Gravit. 50, 46 (2018), arXiv: 1801.03208.

    Article  ADS  Google Scholar 

  44. E. Berti, K. Yagi, H. Yang, and N. Yunes, Gen. Relativ. Gravit. 50, 49 (2018), arXiv: 1801.03587.

    Article  ADS  Google Scholar 

  45. S. Shankaranarayanan, and J. P. Johnson, Gen. Relativ. Gravit. 54, 44 (2022), arXiv: 2204.06533.

    Article  ADS  Google Scholar 

  46. E. Poisson, A. Pound, and I. Vega, Living Rev. Relativ. 14, 7 (2011), arXiv: 1102.0529.

    Article  ADS  Google Scholar 

  47. R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).

    Book  MATH  Google Scholar 

  48. T. Damour, Phys. Rev. D 94, 104015 (2016), arXiv: 1609.00354.

    Article  ADS  MathSciNet  Google Scholar 

  49. D. Bini, and T. Damour, Phys. Rev. D 96, 104038 (2017), arXiv: 1709.00590.

    Article  ADS  MathSciNet  Google Scholar 

  50. X. He, M. Sun, J. Jing, and Z. Cao, Eur. Phys. J. C 81, 97 (2021).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Wentao Liu, Xiongjun Fang & Jiliang Jing

  2. GCAP-CASPER, Department of Physics, Baylor University, Waco, 76798-7316, USA

    Xiongjun Fang & Anzhong Wang

Authors
  1. Wentao Liu
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  2. Xiongjun Fang
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  3. Jiliang Jing
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  4. Anzhong Wang
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Corresponding author

Correspondence to Xiongjun Fang.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2020YFC2201503), National Natural Science Foundation of China (Grant Nos. 11705053, 11975203, and 12035005), and Hunan Provincial Natural Science Foundation of China (Grant No. 2022JJ40262). The work of Xiongjun Fang was supported in part by China Scholarship Council for the Visiting Post-doc Program at Baylor University. We would like very much to thank Xiaokai He and Tao Zhu for valuable discussions, and also thank Zhucun Li.

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The supporting information is available online at http://phys.scichina.com and https://link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

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Liu, W., Fang, X., Jing, J. et al. Gauge invariant perturbations of general spherically symmetric spacetimes. Sci. China Phys. Mech. Astron. 66, 210411 (2023). https://doi.org/10.1007/s11433-022-1956-4

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  • DOI: https://doi.org/10.1007/s11433-022-1956-4

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