No Access

Four-dimensional Lorentzian plane symmetric static Ricci solitons

School of Electrical Engineering and Computer Science, National University of Sciences and Technology, H-12 Campus, Islamabad, Pakistan

E-mail Address: ibrar.hussain@seecs.nust.edu.pk

Search for more papers by this author

Tahirullah

Department of Mathematics, University of Peshawar, Peshawar, KPK, Pakistan

E-mail Address: tahirullah73@hotmail.com

Search for more papers by this author

, and

Suhail Khan

Department of Mathematics, University of Peshawar, Peshawar, KPK, Pakistan

E-mail Address: suhail74pk@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0218271820400106Cited by:7 (Source: Crossref)

This article is part of the issue:

SPECIAL ISSUE — Selected Papers of the Sixth Italian-Pakistani Workshop on Relativistic Astrophysics
Editors: F. De Paolis, I. Hussain, M. A. H. MacCallum and A. Qadir

Abstract

Our focus is to investigate the Ricci solitons of the plane symmetric and static four-dimensional Lorentzian metrics. It is found that these metrics admit shrinking and concircular potential Ricci soliton vector fields with either 6- or 10-dimensional Lie algebra. Further, it is observed that the 4-dimensional Lorentzian static Ricci soliton manifolds are Einsteinian and hence the Ricci solitons are the trivial Ricci solitons.

Keywords:

PACS: 04.20.−q, 02.40.Ky

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. R. S. Hamilton, Contemporary Mathematics, Vol. 71 (American Mathematical Society, Providence, RI, 1988), p. 237. Google Scholar
2. R. S. Hamilton, J. Differ. Geom. 38 (1993) 1. Crossref, Web of Science, Google Scholar
3. R. S. Hamilton, J. Differ. Geom. 37 (1993) 225. Crossref, Web of Science, Google Scholar
4. J. W. Morgan and G. G. Tian, Ricci Flow and the Poincaé Conjecture, Clay Mathematics Monographs (AMS, Providence, 2007). Google Scholar
5. F. Yang, Z. Wang and L. Zhang, arXiv:1707.04846v1 [math.DG]. Google Scholar
6. M. M. Akbar and M. A. H. MacCallum, Phys. Rev. D 92 (2015) 063017. Crossref, Web of Science, ADS, Google Scholar
7. K. Onda, Geom. Ded. 147 (2010) 313. Crossref, Web of Science, Google Scholar
8. W. Batat and K. Onda, Res. Math. 64 (2013) 253. Crossref, Web of Science, Google Scholar
9. G. Calvaruso and A. Fino, Int. J. Geom. Meth. Mod. Phys. 12 (2015) 1550056. Link, Web of Science, Google Scholar
10. U. Sheikh, arXiv:1709.02138v2 [gr-qc]. Google Scholar
11. M. M. Akbar and E. Woolgar, Class. Quantum Grav. 26 (2009) 055015. Crossref, Web of Science, Google Scholar
12. D. H. Friedan, Anal. Phys. 163 (1985) 318. Crossref, Web of Science, ADS, Google Scholar
13. S. I. Vacaru, arXiv:1903.04920v2 [physics.gen-ph]. Google Scholar
14. H. D. Cao, Elliptic and Parabolic Methods in Geometry (A K Peters, Wellesley, MA, 1996), p. 1. Google Scholar
15. M. Brozos-Vázquez, E. García-Río and S. Gavino-Fernández, J. Geom. Anal. 23 (2013) 1196. Crossref, Web of Science, Google Scholar
16. D. Ramos, arXiv:1304.6391v1 [math.DG]. Google Scholar
17. S. Brendle, J. Diff. Geom. 97 (2014) 191. Crossref, Web of Science, Google Scholar
18. B.-Y. Chen, Bull. Korean Math. Soc. 52 (2015) 1535. Crossref, Web of Science, Google Scholar
19. K. L. Duggal, Int. Schol. Rese. Not. 26 (2016) 4903520. Google Scholar
20. K. L. Duggal, Int. Elec. J. Geom. 10 (2017) 1. Crossref, Google Scholar
21. T. Feroze, A. Qadir and M. Ziad, J. Math. Phys. 42 (2001) 4947. Crossref, Web of Science, ADS, Google Scholar
22. M. Ziad, Nuovo Cimento B 114 (1999) 683. ADS, Google Scholar
23. T. Hussain, S. Khan, A. H. Bokhari and G. A. Khan, Theo. Math. Phys. 191 (2017) 620. Crossref, Web of Science, Google Scholar
24. G. S. Hall, Symmetries and Curvature Structure in General Relativity (World Scientific, 2004). Link, Google Scholar
25. I. Hussain, A. Qadir and K. Saifullah, Int. J. Mod. Phys. D 14 (2005) 1431. Link, Web of Science, ADS, Google Scholar
26. U. Camci, I. Hussai and Y. Kucukakca, J. Geom. Phys. 59 (2009) 1476. Crossref, Web of Science, ADS, Google Scholar
27. B.-Y. Chen and S. Deshmukh, Balkan J. Geom. Appl. 19 (2014) 13. Web of Science, Google Scholar
28. S. Pigola, M. Rigoli, M. Rimoldi and A. G. Setti, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 10 (2011) 757. Web of Science, Google Scholar
29. A. Fialkow, Trans. Amer. Math. Soc. 45 (1939) 443. Crossref, Google Scholar
30. S. Khan, A. Mahmood and A. T. Ali, Int. J. Geom. Meth. Mod. Phys. 15 (2018) 1850126. Link, Web of Science, Google Scholar
31. A. T. Ali and S. Khan, Eur. Phys. J. Plus. 131 (2016) 115. Crossref, Web of Science, Google Scholar
32. K. Yano, Proc. Imp. Acad. Tokyo 16 (1940) 195. Crossref, Google Scholar
33. H. Stephani, D. Kramer, M. Maccallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einsteins Field Equations, 2nd edn. (Cambridge University Press, England, 2003). Crossref, Google Scholar
34. B.-Y. Chen and S. Deshmukh, Balkan J. Geom. Appl. 20 (2015) 14. Google Scholar