Skip to main content
SpringerLink
Log in

Conformal Ricci solitons on Vaidya spacetime

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The present paper focused on Vaidya spacetime admitting a conformal Ricci soliton. We derive the expressions for the four components of the associated vector field V and demonstrate that, under this condition, the spacetime reduces to the Schwarzschild spacetime. Furthermore, we determine the necessary expression for the potential function f to establish the existence of a conformal gradient Ricci soliton in the Vaidya spacetime and we provide the condition for which the soliton is shrinking, steady or expanding.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Hamilton, R.S.: The Ricci flow on surfaces. Contemp. Math. 71, 237–262 (1998)

    Article  MathSciNet  Google Scholar 

  2. Hamilton, R.S.: Three-manifolds with positive Ricci curvature. J. Differ. Geom. 17(2), 255–306 (1982)

    Article  MathSciNet  Google Scholar 

  3. Deshmukh, S., Alsodais, H.: A note on Ricci solitons. Symmetry 12(2), 289 (2020)

    Article  ADS  Google Scholar 

  4. Nurowski, P., Randall, M.: Generalized Ricci solitons. J. Geom. Anal. 26, 1280–1345 (2016)

    Article  MathSciNet  Google Scholar 

  5. Yoldas, H.I.: Some classes of Ricci solitons on Lorentzian \(\alpha \)-Sasakian manifolds. Differ. Geom.-Dyn. Syst. 24, 232–244 (2022)

    MathSciNet  Google Scholar 

  6. Ali, A.T., Khan, S.: Ricci soliton vector fields of Kantowski–Sachs spacetimes. Mod. Phys. Lett. A 37(22), 2250146 (2022)

    Article  MathSciNet  ADS  Google Scholar 

  7. Cao, H.D.: Geometry of Ricci solitons. Chin. Ann. Math. Ser. B 27(2), 121–142 (2006)

    Article  MathSciNet  Google Scholar 

  8. Duggal, K.L.: Almost Ricci solitons and physical applications. Int. Electron. J. Geom. 10(2), 1–10 (2017)

    MathSciNet  Google Scholar 

  9. Khatri, M., Chhakchhuak, Z., Lalduhawma, L.P.: Existence of Ricci soliton vector fields on Vaidya spacetime. Phys. Scr. (2023). https://doi.org/10.1088/1402-4896/acff2a

    Article  Google Scholar 

  10. Perrone, D.: Geodesic Ricci solitons on unit tangent sphere bundles. Ann. Glob. Anal. Geom. 44(2), 91–103 (2013)

    Article  MathSciNet  Google Scholar 

  11. Catino, G., Mastrolia, P., Monticelli, D., Rigoli, M.: Analytic and geometric properties of generic Ricci solitons. Trans. Am. Math. Soc. 368(11), 7533–7549 (2016)

    Article  MathSciNet  Google Scholar 

  12. Basu, N., Bhattacharyya, A.: Conformal Ricci soliton in Kenmotsu manifold. Glob. J. Adv. Res. Class. Mod. Geom. 4(1), 15–21 (2015)

    MathSciNet  Google Scholar 

  13. Fischer, A.E.: An introduction to conformal Ricci flow. Class. Quantum Gravity 21(3), S171 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  14. Siddiqi, M.D., Siddiqui, S.A.: Conformal Ricci soliton and Geometrical structure in a perfect fluid spacetime. Int. J. Geom. Methods Mod. Phys. 17(06), 2050083 (2020)

    Article  MathSciNet  Google Scholar 

  15. Dey, S.: Conformal Ricci soliton and almost conformal Ricci soliton in paracontact geometry. Int. J. Geom. Methods Mod. Phys. 20(03), 2350041 (2023)

    Article  MathSciNet  Google Scholar 

  16. Ganguly, D., Dey, S., Ali, A., Bhattacharyya, A.: Conformal Ricci soliton and Quasi–Yamabe soliton on generalized Sasakian space form. J. Geom. Phys. 169, 104339 (2021)

    Article  MathSciNet  Google Scholar 

  17. Khatri, M., Zosangzuala, C., Singh, J.P.: Isometries on almost Ricci–Yamabe solitons. Arab. J. Math. 12, 127–138 (2023)

    Article  Google Scholar 

  18. Li, Y., Ganguly, D.: Kenmotsu metric as conformal \(\eta \)-Ricci soliton. Mediterr. J. Math. 20(4), 193 (2023)

    Article  MathSciNet  Google Scholar 

  19. Li, Y.L., Ganguly, D., Dey, S., Bhattacharyya, A.: Conformal \(\eta \)-Ricci solitons within the framework of indefinite Kenmotsu manifolds. AIMS Math. 7(4), 5408–30 (2022)

    Article  MathSciNet  Google Scholar 

  20. Li, Y., Srivastava, S.K., Mofarreh, F., Kumar, A., Ali, A.: Ricci soliton of CR-warped product manifolds and their classifications. Symmetry 15(5), 976 (2023)

    Article  ADS  Google Scholar 

  21. Catino, G., Mastrolia, P., Monticelli, D.D., Rigoli, M.: Conformal Ricci solitons and related integrability conditions. Adv. Geom. 16(3), 301–328 (2016)

    Article  MathSciNet  Google Scholar 

  22. Chen, Z., Li, Y., Sarkar, S., Dey, S., Bhattacharyya, A.: Ricci soliton and certain related metrics on a three-dimensional trans-Sasakian manifold. Universe 8(11), 595 (2022)

    Article  CAS  ADS  Google Scholar 

  23. Griffiths, J.B., Podolsky, J.: Exact Space-Times in Einstein’s General Relativity. Cambridge University Press, Cambridge (2009)

  24. Hashimoto, K., Iizuka, N., Matsuo, Y.: Islands in Schwarzschild black holes. J. High Energy Phys. 2020, 85 (2020)

    Article  MathSciNet  Google Scholar 

  25. Lindquist, R.W., Schwartz, R.A., Misner, C.W.: Vaidya’s radiating Schwarzschild metric. Phys. Rev. 137, B1364 (1958)

    Article  MathSciNet  Google Scholar 

  26. Simpson, A., Visser, M.: Black-bounce to traversable wormhole. J. Cosmol. Astropart. Phys. 2019(02), 042 (2019)

    Article  MathSciNet  Google Scholar 

  27. Vishveshwara, C.: Scattering of gravitational radiation by a Schwarzschild black-hole. Nature 227, 936–938 (1970)

    Article  CAS  PubMed  ADS  Google Scholar 

  28. Vaidya, P.C.: Nonstatic solutions of Einstein’s field equations for spheres of fluids radiating energy. Phys. Rev. 83, 10 (1951)

    Article  MathSciNet  ADS  Google Scholar 

  29. Vaidya, P.C.: The gravitational field of a radiating star. Gen. Relativ. Gravit. 31, 121 (1999)

    Article  ADS  Google Scholar 

  30. Vaidya, P.C.: The external field of a radiating star in relativity. Gen. Relativ. Gravit. 31, 119 (1999)

    Article  ADS  Google Scholar 

  31. Shaikh, A.A., Kundu, H., Sen, J.: Curvature properties of the Vaidya metric. Indian J. Math. 61(1), 41–59 (2019)

    MathSciNet  Google Scholar 

  32. Dwivedi, I.H., Joshi, P.S.: On the naked singularities of Vaidya spacetime. Class. Quantum Gravity 6, 1599–1606 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  33. Piesnack, J., Kassner, K.: The Vaidya metric: expected and unexpected traits of evaporating black holes. Am. J. Phys. 90(1), 37–46 (2022)

    Article  ADS  Google Scholar 

  34. Rudra, P., Faizal, M., Ali, A.F.: Vaidya spacetime for Galileon gravity’s rainbow. Nucl. Phys. B 909, 725–736 (2016)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  35. Simpson, A., Martin-Moruno, P., Visser, M.: Vaidya spacetimes, black-bounces and traversable wormholes. Class. Quantum Gravity 36(14), 145007 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  36. Virbhadra, K.S.: Energy and momentum in Vaidya spacetime. Pramana-J. Phys. 38(1), 31–35 (1992)

    Article  ADS  Google Scholar 

  37. Sidhoumi, N., Batat, W.: Ricci solitons on four-dimensional Lorentzian Walker manifolds. Adv. Geom. 17(4), 397–406 (2017)

    Article  MathSciNet  Google Scholar 

  38. Chaubey, S.K.: Characterization of perfect fluid spacetimes admitting gradient \(\eta \)-Ricci and gradient Einstein solitons. J. Geom. Phys. 162, 104069 (2021)

    Article  MathSciNet  Google Scholar 

  39. De, K., De, U.C., Syied, A.A., Turki, N.B., Alsaeed, S.: Perfect fluid spacetimes and gradient solitons. J. Nonlinear Math. Phys. 29, 843–858 (2022)

  40. De, U.C., Chaubey, S.K., Shenawy, S.: Perfect fluid spacetimes and Yamabe solitons. J. Math. Phys. 62, 032501 (2021)

  41. G\(\ddot{u}\)ler, S., \({\ddot{U}}\)nal, B.: The existence of gradient Yamabe solitons on spacetimes. Results Math. 77, 206 (2022)

  42. Mandal, S.: Solitons in curved spacetime. EPL 136(1), 11001 (2021)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

The authors express their heartfelt gratitude to the Editor and the anonymous referees for their time and recommendations for improving the manuscript. The first author is thankful to the Ministry of Tribal Affairs, Government of India for financial support in the form of NFST Fellowship (202122-NFST-MIZ-00195).

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mizoram University, Aizawl, Mizoram, 796004, India

    Zosangzuala Chhakchhuak

  2. Department of Mathematics, Central University of South Bihar, Fatehpur, Gaya, Bihar, 824236, India

    Jay Prakash Singh

Authors
  1. Zosangzuala Chhakchhuak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jay Prakash Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization, CZ; Formal analysis, CZ and JPS; Methodology, CZ; Writing-original draft, CZ; Writing-review and editing, CZ; Validation, CZ and JPS. All authors have read and agreed to the final format of the manuscript.

Corresponding author

Correspondence to Zosangzuala Chhakchhuak.

Ethics declarations

Conflict of interest

The authors declare no conflict of interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chhakchhuak, Z., Singh, J.P. Conformal Ricci solitons on Vaidya spacetime. Gen Relativ Gravit 56, 11 (2024). https://doi.org/10.1007/s10714-023-03192-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-023-03192-7

Keywords

Mathematics Subject Classification

Search

Navigation