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Thermodynamics and Null Geodesics of a Bardeen Black Hole Surrounded by Quintessence

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Abstract

We study the thermodynamics of a Bardeen black hole surrounded by quintessence, and we analyze null geodesics and all kinds of orbits corresponding to the energy levels for this black hole. Using the thermodynamical laws of the black holes, we derive the thermodynamic properties and investigate the mass, temperature and heat capacity as functions of entropy. We also study the circular orbits, calculate the deflection angle of photons and compare our results with those obtained for the Schwarzschild black hole surrounded by quintessence matter.

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References

  1. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  Google Scholar 

  2. J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  3. J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973).

    Article  ADS  Google Scholar 

  4. S. Perlmutter et al., Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys. J. 517, 565 (1999).

    Article  ADS  MATH  Google Scholar 

  5. A. G. Riess et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  6. BVRI Light Curves for 22 Type Ia Supernovae, Astron. J. 117, 707 (1999).

  7. D. N. Spergel et al., Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology, Astrophys. J. Suppl. 170, 377 (2007).

    Article  Google Scholar 

  8. M. Tegmark et al., Cosmological parameters from SDSS andWMAP, Phys. Rev. D 69, 103501 (2004).

    Article  ADS  Google Scholar 

  9. U. Seljak et al., Cosmological parameter analysis including SDSS Lya forest and galaxy bias: Constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy, Phys. Rev. D 71, 103515 (2005).

    Article  ADS  Google Scholar 

  10. T. Padmanabham, Cosmological constant-the weight of the vacuum, Phys. Rep. 380, 235 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  11. S. M. Carroll, Quintessence and the Rest of the World: Suppressing Long-Range Interactions, Phys. Rev. Lett. 81, 3067 (1998).

    Article  ADS  Google Scholar 

  12. J. Khoury and A. Weltman, Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space, Phys. Rev. Lett. 93, 171104 (2004).

    Article  ADS  Google Scholar 

  13. C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Dynamical Solution to the Problem of a Small Cosmological Constant and Late-Time Cosmic Acceleration, Phys. Rev. Lett. 85, 4438 (2000).

    Article  ADS  Google Scholar 

  14. T. Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys. Rev. D 66, 021301 (2002).

    Article  ADS  Google Scholar 

  15. R. R. Caldwell, A phantom menace Cosmological consequences of a dark energy component with super-negative equation of state, Phys. Lett. B 545, 23 (2002).

    Article  ADS  Google Scholar 

  16. M. Gasperini, M. Piassa, and G. Veneziano, Quintessence as a runaway dilaton, Phys. Rev. D 65, 023508 (2002).

    Article  ADS  Google Scholar 

  17. E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of Dark energy, Int. Jour. Modern. Phys. D 15, 1753 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. V. Kiselev, Quintessence and BHs, Class. Quan. Grav. 20, 1187 (2003).

    Article  ADS  MATH  Google Scholar 

  19. B. Malakolkalami and K. Ghaderi, The null geodesics of the ReissnerNordstrm BH surrounded by quintessence, Mod. Phys. Lett. A 30, 1550049 (2015).

    Article  ADS  Google Scholar 

  20. B. Malakolkalami and K. Ghaderi, Schwarzschildanti de Sitter BH with quintessence, Astrophys. Space Sci. 357, 112 (2015).

    Article  ADS  Google Scholar 

  21. S. Fernando, Schwarzschild black hole surrounded by quintessence: Null geodesics, Gen. Rel. Grav. 44, 1857 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. J. M. Bardeen, Non-singular general-relativistic gravitational collapse, in Proceedings of International Conference GR5 (USSR, Tbilisi, Georgia, 1968), p.174.

    Google Scholar 

  23. E. Ayon-Beato and A. Garcia, The Bardeen model as a nonlinear magnetic monopole, Phys. Lett. B. 493, 149 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. K. A. Bronnikov, Comment on Regular black holes in general relativity coupled to nonlinear electrodynamics, Phys. Rev. Lett. 85, 4641 (2000).

    Article  ADS  Google Scholar 

  25. K. A. Bronnikov, Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev. D 63, 044005 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  26. V. Cardoso, A. S. Miranda, E. Berti, H. Witeck, and V. T. Zanchin, Geodesics stability, Lyapunov exponents and quasinormal modes, Phys. Rev. D 79, 064016 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  27. P. Amore and S. Arceo, Analytical formulas for gravitational lensing, Phys. Rev. D 73, 083004 (2006).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Marivan Branch, Islamic Azad University, Marivan, Iran

    K. Ghaderi

  2. Department of Physics, University of Kurdistan, Pasdaran st., Sanandaj, Iran

    B. Malakolkalami

Authors
  1. K. Ghaderi
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  2. B. Malakolkalami
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Correspondence to K. Ghaderi.

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Ghaderi, K., Malakolkalami, B. Thermodynamics and Null Geodesics of a Bardeen Black Hole Surrounded by Quintessence. Gravit. Cosmol. 24, 61–70 (2018). https://doi.org/10.1134/S0202289318010073

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  • DOI: https://doi.org/10.1134/S0202289318010073

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