Black holes with quintessence in pure Lovelock gravity

  • J. M. ToledoEmail author
  • V. B. Bezerra
Research Article


In this work, we obtain the solution corresponding to a static spherically symmetric black hole surrounded by quintessence in pure Lovelock gravity. Some aspects of the thermodynamics of this black hole are investigated, with special emphasis on the Hawking temperature, entropy and heat capacity. The behaviors of these quantities are analyzed and the differences with respect to the ones in the Theory of General Relativity are pointed out.


Black holes Lovelock gravity Quintessence Thermodynamics 



V. B. Bezerra is partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) through the research Project nr. 305835/2016-5.


  1. 1.
    Lovelock, D.: The einstein tensor and its generalizations. J. Math. Phys. 12(3), 498 (1971)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Zwiebach, B.: Curvature squared terms and string theories. Phys. Lett. B 156(5–6), 315 (1985)ADSCrossRefGoogle Scholar
  3. 3.
    Nojiri, S., Odintsov, S., Oikonomou, V.: Modified gravity theories on a nutshell: inflation, bounce and late-time evolution, arXiv preprint arXiv:1705.11098 (2017)
  4. 4.
    Boulware, D.G., Deser, S.: String-generated gravity models. Phys. Rev. Lett. 55(24), 2656 (1985)ADSCrossRefGoogle Scholar
  5. 5.
    Dadhich, N., Ghosh, S.G., Jhingan, S.: Bound orbits and gravitational theory. Phys. Rev. D 88(12), 124040 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    Dadhich, N., Pons, J.M.: Probing pure lovelock gravity by Nariai and Bertotti–Robinson solutions. J. Math. Phys. 54(10), 102501 (2013)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Dadhich, N., Pons, J.M., Prabhu, K.: Thermodynamical universality of the Lovelock black holes. Gen. Relat. Gravit. 44(10), 2595 (2012)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Abbott, B.P., Abbott, R., Abbott, T., Abernathy, M., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R., et al.: Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Wheeler, J.T.: Symmetric solutions to the Gauss–Bonnet extended Einstein equations. Nucl. Phys. B 268(3–4), 737 (1986)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Cai, R.G.: A note on thermodynamics of black holes in Lovelock gravity. Phys. Lett. B 582(3), 237 (2004)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Hennigar, R.A., Tjoa, E., Mann, R.B.: Thermodynamics of hairy black holes in Lovelock gravity. J. High Energy Phys. 2017(2), 70 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hennigar, R.A., Mann, R.B., Tjoa, E.: Superfluid black holes. Phys. Rev. Lett. 118(2), 021301 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    Myers, R.C., Simon, J.Z.: Black-hole thermodynamics in Lovelock gravity. Phys. Rev. D 38(8), 2434 (1988)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Herscovich, E., Richarte, M.G.: Black holes in Einstein–Gauss–Bonnet gravity with a string cloud background. Phys. Lett. B 689(4), 192 (2010)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Ghosh, S.G., Papnoi, U., Maharaj, S.D.: Cloud of strings in third order Lovelock gravity. Phys. Rev. D 90(4), 044068 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    Lee, T.H., Baboolal, D., Ghosh, S.G.: Lovelock black holes in a string cloud background. Eur. Phys. J. C 75(7), 297 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    Ghosh, S.G., Maharaj, S.D., Baboolal, D., Lee, T.H.: Lovelock black holes surrounded by quintessence. Eur. Phys. J. C 78(2), 90 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    Ghosh, S.G., Amir, M., Maharaj, S.D.: Quintessence background for 5D Einstein–Gauss–Bonnet black holes. Eur. Phys. J. C 77(8), 530 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    Whitt, B.: Spherically symmetric solutions of general second-order gravity. Phys. Rev. D 38(10), 3000 (1988)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Wiltshire, D.: Spherically symmetric solutions of Einstein–Maxwell theory with a Gauss–Bonnet term. Phys. Lett. B 169(1), 36 (1986)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Graça, J.M., Salako, G.I., Bezerra, V.B.: Quasinormal modes of a black hole with a cloud of strings in Einstein–Gauss–Bonnet gravity. Int. J. Mod. Phys. D 26(10), 1750113 (2017)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Cai, R.G., Ohta, N.: Black holes in pure Lovelock gravities. Phys. Rev. D 74(6), 064001 (2006)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Camanho, X.O., Edelstein, J.D.: A Lovelock black hole bestiary. Class. Quantum Gravity 30(3), 035009 (2013)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Ade, P.A., Aghanim, N., Alves, M., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Aussel, H., Baccigalupi, C., et al.: Planck 2013 results. I. Overview of products and scientific results. Astron. Astrophys. 571, A1 (2014)CrossRefGoogle Scholar
  25. 25.
    Caldwell, R.: An introduction to quintessence. Braz. J. Phys. 30(2), 215 (2000)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Lima, J.A.S.: Alternative dark energy models: an overview. Braz. J. Phys. 34(1A), 194 (2004)ADSCrossRefGoogle Scholar
  27. 27.
    Liu, M., Lu, J., Gui, Y.: The influence of free quintessence on gravitational frequency shift and deflection of light with 4D momentum. Eur. Phys. J. C 59(1), 107 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    Kiselev, V.V.: Quintessence and black holes. Class. Quantum Gravity 20(6), 1187 (2003)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Ghosh, S.G.: Rotating black hole and quintessence. Eur. Phys. J. C 76(4), 1 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    Toshmatov, B., Stuchlík, Z., Ahmedov, B.: Rotating black hole solutions with quintessential energy. Eur. Phys. J. Plus 132(2), 98 (2017)CrossRefGoogle Scholar
  31. 31.
    Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Commun. Math. Phys. 31(2), 161 (1973)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7(8), 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43(3), 199 (1975)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Dadhich, N.: A distinguishing gravitational property for gravitational equation in higher dimensions. Eur. Phys. J. C 76(3), 104 (2016)ADSCrossRefGoogle Scholar
  35. 35.
    Ghosh, S.G., Maharaj, S.D.: Cloud of strings for radiating black holes in Lovelock gravity. Phys. Rev. D 89(8), 084027 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    Dadhich, N., Hansraj, S., Chilambwe, B.: Compact objects in pure Lovelock theory. Int. J. Mod. Phys. D 26(06), 1750056 (2017)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Dadhich, N.: Characterization of the Lovelock gravity by Bianchi derivative. Pramana 74(6), 875 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    Dadhich, N., Ghosh, S.G., Jhingan, S.: The Lovelock gravity in the critical spacetime dimension. Phys. Lett. B 711(2), 196 (2012)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Dadhich, N.: On lovelock vacuum solution, arXiv preprint arXiv:1006.0337 (2010)
  40. 40.
    Dolan, B.P.: The cosmological constant and black-hole thermodynamic potentials. Class. Quantum Gravity 28(12), 125020 (2011)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations