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Correction to the conservation laws in plane symmetric gravitational wave-like spacetimes

Farhad Ali

Department of Mathematics, Kohat University of Science and Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan

E-mail Address: farhadmardan@gmail.com

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Wali Khan Mashwani

Department of Mathematics, Kohat University of Science and Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan

E-mail Address: mashwanigr8@gmail.com

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, and

Muhammad Asif Jan

Department of Mathematics, Kohat University of Science and Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan

E-mail Address: majan.math@gmail.com

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https://doi.org/10.1142/S0217732318501237Cited by:5 (Source: Crossref)

Abstract

This paper discusses the approximate Noether symmetries of the action of plane symmetric spacetime. A time-dependent conformal factor is introduced in the plane symmetric metric in such a way so as to obtain the same number of Noether symmetries as for the exact plane symmetric spacetime. The corresponding approximate conservation is obtained to discuss the conservation laws of the energy and momentum during the formation of gravitational wave.

Keywords:

PACS: 04.20.Fy, 04.20.Jb

References

1. N. Nissani and E. Leibowitz, Int. J. Theor. Phys. 30, 837 (1991). Crossref, Web of Science, Google Scholar
2. R. Dick, Int. J. Theor. Phys. 2, 109 (1993). Crossref, Web of Science, Google Scholar
3. G. J. Olmo, Int. J. Mod. Phys. D 20, 413 (2011). Link, Web of Science, ADS, Google Scholar
4. A. N. Petrov and R. R. Lompay, Gen. Relat. Gravit. 45, 545 (2013). Crossref, Web of Science, ADS, Google Scholar
5. P. L. McGrath, M. Chanona, R. J. Epp, M. J. Koop and R. B. Mann, Class. Quantum Grav. 31, 095006 (2014). Crossref, Web of Science, Google Scholar
6. G. Sardanashvily, Int. J. Geom. Methods Mod. Phys. 13, 1650086 (2016). Link, Web of Science, Google Scholar
7. LIGO Scientific Collab. and Virgo Collab. (B. P. Abbott et al.), Phys. Rev. Lett. 116, 241102 (2016). Crossref, Web of Science, ADS, Google Scholar
8. The LIGO Scientific Collab. and The Virgo Collab., An improved analysis of GW150914 using a fully spin-precessing waveform model, arXiv:1606.01210. Google Scholar
9. K. S. Thorne, Rev. Mod. Phys. 52, 285 (1980). Crossref, Web of Science, ADS, Google Scholar
10. D. N. Page, Phys. Rev. Lett. 71, 3743 (1993). Crossref, Web of Science, ADS, Google Scholar
11. N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations (John Wiley & Sons, 1999). Google Scholar
12. D. Kramer, H. Stephani, M. A. H. MacCallum and E. Herlt, Exact Solution of Einstein Field Equations (Cambridge Univ. Press, 1980). Google Scholar
13. P. G. L. Leach, S. Moyo, S. Cotsakis and R. L. Lemmer, J. Nonlinear Math. Phys. 8, 139 (2001). Crossref, Web of Science, ADS, Google Scholar
14. G. Unal, Phys. Lett. A 269, 13 (2000). Crossref, Web of Science, ADS, Google Scholar
15. G. Unal, C. M. Khalique and G. F. Alisverisçi, Quaest. Math. 30, 483 (2009). Crossref, Web of Science, Google Scholar
16. G. Unal and C. M. Khalique, Quaest. Math. 28, 305 (2005). Crossref, Google Scholar
17. U. Camc and A. Yildirim, Phys. Scripta 89, 084003 (2014). Crossref, Web of Science, Google Scholar
18. G. Baumann, Symmetry Analysis of Differential Equations with Mathematica (Springer-Verlag, 2000). Crossref, Google Scholar
19. G. D. Birkhoff, Relativity and Modern Physics (Harvard Univ. Press, 1923). Google Scholar
20. G. W. Bluman and S. Kumei, Symmetries and Differential Equations (Springer-Verlag, 1989). Crossref, Google Scholar
21. G. W. Bluman, A. F. Cheviakov and S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations (Springer Science, 2010). Crossref, Google Scholar
22. T. H. Boyer, Am. J. Phys. 34, 475 (1966). Crossref, Web of Science, ADS, Google Scholar
23. E. Noether, Nachr. Ges. Wiss. Göttingen 2, 235 (1918). Google Scholar
24. H. A. Al-Kuwari and M. O. Taha, Am. J. Phys. 59, 363 (1991). Crossref, Web of Science, ADS, Google Scholar
25. F. Ali, Appl. Math. Sci. 8, 4697 (2014). Crossref, Google Scholar
26. F. Ali and T. Feroze, Int. J. Theor. Phys. 52, 3329 (2013). Crossref, Web of Science, Google Scholar
27. F. Ali, T. Feroze and S. Ali, Theor. Math. Phys. 184, 92 (2015). Crossref, Web of Science, Google Scholar
28. F. Ali and T. Feroze, Mathematics 4, 50 (2016). Crossref, Web of Science, Google Scholar
29. B. Jamil and T. Feroze, Int. J. Mod. Phys. D 26, 1741006 (2017). Link, Web of Science, ADS, Google Scholar
30. U. Camci and A. Yildirim, Int. J. Geom. Methods Mod. Phys. 12, 1550120 (2015). Link, Web of Science, Google Scholar
31. S. Jamal and G. Shabbir, Int. J. Geom. Methods Mod. Phys. 13, 1650109 (2016). Link, Web of Science, Google Scholar
32. R. Maartens and S. D. Maharaj, Class. Quantum Grav. 8, 503 (1991). Crossref, Web of Science, ADS, Google Scholar
33. A. Einstein and N. Rosen, J. Franklin Inst. 223, 43 (1937). Crossref, ADS, Google Scholar
34. J. Ehlers, A. Rosenblum, J. Goldberge and P. Havas, Astrophys. J. Lett. 208, L77 (1976). Crossref, Web of Science, ADS, Google Scholar
35. V. D. Zakharov, Gravitational Waves in Einstein’s Theory (Halsted Press, 1973), translated from Russian by R. N. Sen. Google Scholar
36. A. H. Taub, Ann. Math. 53(3), 472–490 (1951). Crossref, Web of Science, ADS, Google Scholar
37. U. Camci, J. Cosmol. Astropart. Phys. 07, 002 (2014). Crossref, Web of Science, ADS, Google Scholar
38. S. Capozziello, R. De Ritis and P. Scudellaro, Int. J. Mod. Phys. D 3, 609 (1994). Link, Web of Science, ADS, Google Scholar
39. S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C 72, Article 2068 (2012). Google Scholar
40. I. Hussain and A. Qadi, Il Nuovo Cimento B 122, 953 (2007). Google Scholar
41. I. Hussain, A. Mahomed and A. Qadir, SIGMA 3, 115 (2007). ADS, Google Scholar
42. F. Ali and T. Feroze, Theor. Math. Phys. 193, 1703 (2017). Crossref, Web of Science, Google Scholar
43. F. Ali and T. Feroze, Int. J. Geom. Methods Mod. Phys. 12, 1550124 (2015). Link, Web of Science, Google Scholar
44. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (W. H. Freeman and Company, 1973). Google Scholar
45. F. Ali, Ph.D. thesis, SNS NUST Islamabad Pakistan (2015), eprints.hec.gov.pk/6447/1/16016S.pdf. Google Scholar