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Strong Gravitational Lensing for the Quantum-Modified Schwarzschild Black Hole

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Abstract

We research the strong gravitational lensing for the quantum-modified Schwarzschild black hole which is derived from quantum Raychaudhuri equation. With the increase of quantum Raychaudhuri equation parameter η, we find that the distance between the black hole and the light passing by it becomes smaller; the deflection angle gets larger; the magnification of relativistic images is more similar; all of the relativistic images move towards the black hole while the images are farther to each other. These results, as we expect, will degenerate to the case of Schwarzschild black hole when \(\eta \rightarrow 0\).

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References

  1. Einstein, A.: Science 84, 506 (1936)

    Article  ADS  Google Scholar 

  2. Darwin, C.: Proc. Roy. Soc. Lond. A 249, 180 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  3. Virbhadra, K.S., Ellis, G.F.R.: Phys. Rev. D 62, 084003 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  4. Bozza, V., Capozziello, S., lovane, G., Scarpetta, G.: Gen. Rel. and Grav. 33, 1535 (2001)

    Article  ADS  Google Scholar 

  5. Bozza, V.: Phys. Rev.D 66, 103001 (2002)

    Article  ADS  Google Scholar 

  6. Eiroa, E.F., Romero, G.E., Torres, D.F.: Phys. Rev. D 66, 024010 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  7. Bozza, V.: Phys. Rev. D 67, 103006 (2003)

    Article  ADS  Google Scholar 

  8. Aliev, A.N., Talazan, P.: Phys. Rev. D 80, 044023 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. Ghosh, T., Sengupta, S.: Phys. Rev. D 81, 044013 (2010)

    Article  ADS  Google Scholar 

  10. Eiroa, E.F., Sendra, C.M.: Phys. Rev. D 88, 103007 (2013)

    Article  ADS  Google Scholar 

  11. Ding, C., Liu, C., Xiao, Y., Jiang, L., Cai, R.: Phys. Rev. D 88, 104007 (2013)

    Article  ADS  Google Scholar 

  12. Wei, S., Liu, Y., Fu, C., Yang, K.: J. Cosmol. Astropart. Phys. 10, 053 (2012)

    Article  ADS  Google Scholar 

  13. Wei, S., Liu, Y.: Phys. Rev. D 85, 064044 (2012)

    Article  ADS  Google Scholar 

  14. Kraniotis, G.V.: Class. Quant. Grav. 28, 085021 (2011)

    Article  ADS  Google Scholar 

  15. Walash, D., Carswell, R.F., Weymann, R.J.: Nature 279, 381 (1979)

  16. Chen, S., Jing, J.: Phys. Rev. D 85, 124029 (2012)

    Article  ADS  Google Scholar 

  17. Ji, L., Chen, S., Jing, J.: J. High Energy Phys. 03, 089 (2014)

    Article  ADS  Google Scholar 

  18. Chen, S., Jing, J.: J. Cosmol. Astropart. Phys. 10, 002 (2015)

    Article  ADS  Google Scholar 

  19. Chen, S., Zhang, L., Jing, J.: Eur. Phys. J. C 78, 981 (2018)

    Article  ADS  Google Scholar 

  20. Zhang, R., Jing, J., Chen, S.: Phys. Rev. D 95, 064054 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhang, R., Jing, J.: Eur. Phys. J. C 78, 796 (2018)

    Article  ADS  Google Scholar 

  22. Ali, A.F., Khalil, M.M.: Nucl. Phys. B 909, 173–185 (2016)

    Article  ADS  Google Scholar 

  23. Qi, D., Liu, L., Liu, S.: Can. J. Phys 97(9), 1012–1018 (2019)

    Article  ADS  Google Scholar 

  24. Vagenas, E.C., Alasfar, L., Alsaleh, S.M., Ali, A.F.: Nucl. Phys. B 931, 72–78 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

Thanks for the support of the National Natural Science Foundation of China under Grant No. 11947076, 11865018; the Talent Introduction Fund (Grant no. 2018BS042) at Henan University of Technology.

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Authors and Affiliations

  1. College of Science, Henan University of Technology, Zhengzhou, Henan, 450001, People’s Republic of China

    Ruanjing Zhang & Jian Lin

  2. School of Physics and Electronic Science, Zunyi Normal University, Zunyi, Guizhou, 563006, People’s Republic of China

    Qihong Huang

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  1. Ruanjing Zhang
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  2. Jian Lin
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Correspondence to Ruanjing Zhang.

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Zhang, R., Lin, J. & Huang, Q. Strong Gravitational Lensing for the Quantum-Modified Schwarzschild Black Hole. Int J Theor Phys 60, 387–396 (2021). https://doi.org/10.1007/s10773-020-04705-9

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  • DOI: https://doi.org/10.1007/s10773-020-04705-9

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