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Effects of dark energy on geodesics and thermodynamics of the Schwarzschild-de Sitter space-time

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Abstract

The effects of quintessence on geodesics and thermodynamics of the Schwarzschild-de Sitter black hole are studied and the results are compared with the case without the presence of quintessence. We show that the presence of quintessence increases the entropy and heat capacity of the Schwarzschild-de Sitter black hole and decreases the mass and temperature of this black hole. In particular, we focused on types of orbits and we found that the coordinate time, circular orbits, period of the circular orbits and the angle of deflection of light for this black hole increase in quintessence field while the quintessence decreases the effective potential, force on the massless particle, Lyapunov exponent \(\lambda \) and closest approach.

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References

  • Ainou, M.A., Rodrigues, M.E.: Thermodynamical, geometrical and Poincar methods for charged black holes in presence of quintessence. J. High Energy Phys. 1309, 146 (2013)

    Article  ADS  Google Scholar 

  • Armendariz-Picon, C., Mukhanov, V., Steinhardt, P.J.: 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 

  • Avelino, P.P.: Quintessence and tachyon dark energy with a constant equation of state parameter. Phys. Lett. B 699, 10 (2011)

    Article  ADS  Google Scholar 

  • Babichev, E.O., Dokuchaev, V.I., Eroshenko, Y.N.: Black holes in the presence of dark energy. Phys. Usp. 56, 1155 (2013)

    Article  ADS  Google Scholar 

  • Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Commun. Math. Phys. 31, 161 (1973)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Caldwell, R.R.: 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  • Carroll, S.M.: Quintessence and the rest of the world: suppressing long-range interactions. Phys. Rev. Lett. 81, 3067 (1998)

    Article  ADS  Google Scholar 

  • Chandraseckar, S.: Mathematical Theory of Black Holes. Oxford University Press, Oxford (1980)

    Google Scholar 

  • Chen, S., Wang, B., Su, R.: Hawking radiation in a d-dimensional static spherically-symmetric black hole surrounded by quintessence. Phys. Rev. D 77, 124011 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  • Chen, S., Pan, Q., Jing, J.: Holographic superconductors in quintessence AdS black hole spacetime. Class. Quantum Gravity 30, 145001 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Copeland, E.J., Sami, M., Tsujikawa, S.: Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Escobar, D., Fadragas, C.R., Leon, G., Leyva, Y.: Phase space analysis of quintessence fields in Randall-Sundrum Braneworld: a refined study. Class. Quantum Gravity 29, 175005 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Farooq, M.U., Jamil, M., Debnath, U.: Dynamics of interacting phantom and quintessence dark energy. Astrophys. Space Sci. 334, 243 (2011)

    Article  ADS  Google Scholar 

  • Fernando, S.: Schwarzschild black hole surrounded by quintessence: null geodesics. Gen. Relativ. Gravit. 44, 1857 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Ghaderi, K., Malakolkalami, B.: Thermodynamics of the Schwarzschild and the Reissner-Nordström black holes with quintessence. Nucl. Phys. B 903, 10 (2016)

    Article  ADS  MATH  Google Scholar 

  • Ghosh, S.G.: Rotating black hole and quintessence. Eur. Phys. J. C 76, 222 (2016)

    Article  ADS  Google Scholar 

  • Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ishwarchandra, N., Ibohal, N., Singh, K.Y.: Schwarzschild black hole in dark energy background. Astrophys. Space Sci. 353, 633 (2014)

    Article  ADS  Google Scholar 

  • Khoury, J., Weltman, A.: Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104 (2004)

    Article  ADS  Google Scholar 

  • Kiselev, V.V.: Quintessence and black holes. Class. Quantum Gravity 20, 1187 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Li, Z., Wang, A.: Existence of black holes in Friedmann-Robertson-Walker universe dominated by dark energy. Mod. Phys. Lett. A 22, 1663 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Li, G.Q., Xiao, S.F.: State equations for massless spin fields in static spherical spacetime filled with quintessence. Gen. Relativ. Gravit. 42, 17191726 (2010)

    MathSciNet  Google Scholar 

  • Lola, S., Pallis, C., Tzelati, E.: Tracking quintessence and cold dark matter candidates. J. Cosmol. Astropart. Phys. 0911, 017 (2009)

    Article  ADS  Google Scholar 

  • Malakolkalami, B., Ghaderi, K.: The null geodesics of the Reissner-Nordström black hole surrounded by quintessence. Mod. Phys. Lett. A 30, 1550049 (2015a)

    Article  ADS  Google Scholar 

  • Malakolkalami, B., Ghaderi, K.: Schwarzschild-anti de Sitter black hole with quintessence. Astrophys. Space Sci. 357, 112 (2015b)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Perlmutter, S., et al.: Measurements of \(\varOmega\) and \(\varLambda\) from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  • Riess, A.G., et al.: Observational evidence from supernovae for an accelerating Universe and a cosmological constant. Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  • Riess, A.G., et al.: BVRI light curves for 22 type Ia supernovae. Astron. J. 117, 707 (1999)

    Article  ADS  Google Scholar 

  • Saleh, M., Bouetou, B.T., Kofane, T.C.: Quasinormal modes and Hawking radiation of a Reissner-Nordström black hole surrounded by quintessence. Astrophys. Space Sci. 333, 449 (2011)

    Article  ADS  MATH  Google Scholar 

  • Saridakis, E.N., Ward, J.: Quintessence and phantom dark energy from ghost D-branes. Phys. Rev. D 80, 083003 (2009)

    Article  ADS  Google Scholar 

  • Seljak, U., et al.: Cosmological parameter analysis including SDSS \(\mbox{Ly}\alpha\) 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 

  • Shojai, F., Moti, R., Najdat, F.: Tracker coupled quintessence. Phys. Rev. D 87, 043007 (2013)

    Article  ADS  Google Scholar 

  • Spergel, D.N., et al.: Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology. Astrophys. J. Suppl. 170, 377 (2007)

    Article  ADS  Google Scholar 

  • Tegmark, M., et al.: Cosmological parameters from SDSS and WMAP. Phys. Rev. D 69, 103501 (2004)

    Article  ADS  Google Scholar 

  • Thomas, B.B., Saleh, M.: Thermodynamics and phase transition of the Reissner-Nordström black hole surrounded by quintessence. Gen. Relativ. Gravit. 44, 2181 (2012)

    Article  ADS  MATH  Google Scholar 

  • Tsujikawa, S.: Quintessence: a review. Class. Quantum Gravity 30, 214003 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Varghese, N., Kuriakose, V.C.: Massive charged scalar quasinormal modes of Reissner-Nordström black hole surrounded by quintessence. Gen. Relativ. Gravit. 41, 1249 (2009)

    Article  ADS  MATH  Google Scholar 

  • Wang, C.Y., Zhang, Y., Gui, Y.X., Lu, J.B.: Dirac quasinormal modes of Reissner-Nordström black hole surrounded by quintessence. Commun. Theor. Phys. 53, 882 (2010)

    Article  ADS  MATH  Google Scholar 

  • Wang, P., Wu, P., Yu, H.: A new extended quintessence. Eur. Phys. J. C 72, 2245 (2012)

    Article  ADS  Google Scholar 

  • Wei, Y.H., Chu, Z.H.: Thermodynamic properties of a Reissner-Nordström quintessence black hole. Chin. Phys. Lett. 28, 100403 (2011)

    Article  ADS  Google Scholar 

  • Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Zhang, Y., Gui, Y.X.: Quasinormal modes of a Schwarzschild black hole surrounded by quintessence. Class. Quantum Gravity 23, 6141 (2006)

    Article  ADS  MATH  Google Scholar 

Download references

Acknowledgements

This work has been supported financially by Marivan Branch, Islamic Azad University, Marivan, Iran.

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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

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  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. Effects of dark energy on geodesics and thermodynamics of the Schwarzschild-de Sitter space-time. Astrophys Space Sci 362, 163 (2017). https://doi.org/10.1007/s10509-017-3143-7

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